Q:

Did Dumbledore believe that Voldemort was redeemable? 

Did Dumbledore ever express his opinions on whether or not he believed Voldemort to be able to find redemption after all that he had done?  I've searched for quotes from Dumbledore regarding Voldemort's fate, but it seems the narrative is almost always framed in the context of Harry having to fight against Voldemort in the end.  At what point, if ever, did Dumbledore decide that Tom Riddle was perhaps beyond saving? 
If we don't have any evidence from Dumbledore's perspective, has Rowling ever commented on a "point of no return" for Voldemort personally, in which he could never come back from the evil he had committed?  Or, has she perhaps commented saying something to the contrary--that no such point existed? 

A:

Dumbledore's attitude to Voldemort changed over the years so my answer takes his position in stages.  His mentality can be characterised as wary suspicion.  He didn't want to isolate Voldemort or push him towards Dark Magic.  But he didn't lie to himself either about the sort of choices Riddle was making and the way he was entrenching himself as evil personified.  In the end, Voldemort was irredeemable. 
Voldemort as a child: Dumbledore decided to keep an eye out. 
At this point Dumbledore had no idea of the monster that Voldemort would turn into. 

“Did I know that I had just met the most dangerous Dark wizard of all time?”  said Dumbledore. “ No, I had no idea that he was to grow up to be what he is.  However, I was certainly intrigued by him.  I returned to Hogwarts intending to keep an eye upon him, something I should have done in any case, given that he was alone and friendless, but which, already, I felt I ought to do for others’ sake as much as his." 
(Half-Blood Prince, Chapter 13, The Secret Riddle). 

As far as Dumbledore was concerned Voldemort was just a powerful kid who was abusing his magical abilities.  However, he believed that Voldemort (just like all other children) could be trained to harness his magic for good. 

“At Hogwarts,” Dumbledore went on, “we teach you not only to use magic, but to control it.  You have — inadvertently, I am sure — been using your powers in a way that is neither taught nor tolerated at our school." 
(Half-Blood Prince, Chapter 13, The Secret Riddle). 

Dumbledore assumes that Voldemort isn't doing anything a good education won't fix.  When Voldemort came to Hogwarts Dumbledore decided not to hold his previous indiscretions against him.  Basically, he chose to give Voldemort the benefit of the doubt. 

“Didn’t you tell them, sir, what he’d been like when you met him at the orphanage?”  asked Harry. 
  “No, I did not.  Though he had shown no hint of remorse, it was possible that he felt sorry for how he had behaved before and was resolved to turn over a fresh leaf.  I chose to give him that chance.” 
(Half-Blood Prince, Chapter 17, A Sluggish Memory). 

Dumbledore chooses to trust Voldemort - but he does also decide to "keep an eye upon him". 
When the Chamber of Secrets was opened he was suspicious. 
We know that Dumbledore never believed that Hagrid was responsible for opening the Chamber of Secrets.  He never openly accused Riddle but Riddle himself seemed to think that Dumbledore had made an educated guess as to who was behind it all. 

“Only the Transfiguration teacher, Dumbledore, seemed to think Hagrid was innocent.  He persuaded Dippet to keep Hagrid and train him as gamekeeper.  Yes, I think Dumbledore might have guessed. ...  Dumbledore never seemed to like me as much as the other teachers did. ...” 
  “I bet Dumbledore saw right through you,” said Harry, his teeth gritted. 
  “Well, he certainly kept an annoyingly close watch on me after Hagrid was expelled,” said Riddle carelessly. 
(Chamber of Secrets, Chapter 17, The Heir of Slytherin). 

The opening of the Chamber of Secrets was only one of a number of "nasty incidents" that Dumbledore suspected that Voldemort and his cronies were behind. 

“Rigidly controlled by Riddle, [the early Death Eaters] were never detected in open wrongdoing, although their seven years at Hogwarts were marked by a number of nasty incidents to which they were never satisfactorily linked, the most serious of which was, of course, the opening of the Chamber of Secrets, which resulted in the death of a girl." 
(Half-Blood Prince, Chapter 17, A Sluggish Memory). 

Dumbledore can see that Voldemort is slipping into evil.  But because he can't definitively prove anything he can't force Voldemort to atone for his actions.  His suspicion of Riddle is high.  Is Voldemort redeemable at this point?  Probably.  But he didn't seem to care much about the advice of Dumbledore or anyone else who might council him to change his ways.  His only goal is the consolation of power as he slips further into the Dark Arts.  He could've reformed himself at this period but Dumbledore never expressed any belief that he would want to.  He was still keeping an eye on Voldemort, which (seeming as Riddle was never caught in wrongdoing) was all that he could really do. 
Voldemort as an adult: Dumbledore could see he was beyond saving. 
The question asks whether there is a 'point of no return' for Voldemort, as far as Dumbledore was concerned.  The time when he goes for an interview at Hogwarts is undoubtedly it.  It marks the turning point where Dumbledore can see clearly that Voldemort is beyond saving. 

“Then we have nothing more to say to each other.” 
  “No, nothing,” said Dumbledore, and a great sadness filled his face. “ The time is long gone when I could frighten you with a burning wardrobe and force you to make repayment for your crimes.  But I wish I could, Tom... I wish I could...”
(Half-Blood Prince, Chapter 13, The Secret Riddle). 

Dumbledore can no longer make Voldemort "make repayment for [his] crimes".  His path is set and there's nothing Dumbledore can do to change it.  That's the realisation that lies behind the sad look on his face.  He sees that the little boy he once taught is gone forever.  Only Voldemort remains.  From this point Dumbledore abandons any hope that he can reform Voldemort and dedicates himself to fighting him. 

Henceforth, he never expressed any hope that Voldemort might change.  However, there were a number of signs that Dumbledore retained his belief that Voldemort was irredeemable:

Dumbledore heard the prophecy and knew that Voldemort had to die. 
When he heard Professor Trelawney's prophecy Dumbledore knew that a confrontation between Harry and Voldemort was possible.  When Voldemort acted on that prophecy by attacking Harry as a baby Voldemort's destiny was set.  Voldemort wasn't going to rest until he defeated his nemesis or was destroyed by him.  That made the prospects for redemption unlikely. 
Voldemort showed no hint that he wanted redemption. 
Throughout the two wizarding wars the body count kind of went up somewhat.  Voldemort continued murdering people with wild abandon.  Dumbledore had no reason to think that he'd want to stop. 
Dumbledore set out to destroy the Horcruxes. 
Dumbledore discovered Voldemort's master secret and set out to destroy his soul pieces one by one.  These are not the actions of someone who's trying to gently persuade their adversary to switch sides. 
The only time they met in the Second Wizarding War, Dumbledore didn't seem to want to talk redemption. 

“You do not seek to kill me, Dumbledore?”  called Voldemort, his scarlet eyes narrowed over the top of the shield. “ Above such brutality, are you?” 
  “We both know that there are other ways of destroying a man, Tom,” Dumbledore said calmly, continuing to walk toward Voldemort as though he had not a fear in the world, as though nothing had happened to interrupt his stroll up the hall. “ Merely taking your life would not satisfy me, I admit-”
(Order of the Phoenix, Chapter 36, The Only One He Ever Feared). 

Voldemort has killed enough people at this people (including people Dumbledore loved) to piss Dumbledore off.  He wasn't in the mood to forgive Voldemort or allow him a second chance.  Even killing Voldemort "wouldn't satisfy" him.  He was committed to destroying his legacy as well as his life, and he had a personal stake in his downfall. 
Because of the Horcruxes, if Voldemort had repented then he might have died anyway. 
Remorse can be fatal for evil wizards:

“Isn’t there any way of putting yourself back together?”  Ron asked. 
  “Yes,” said Hermione with a hollow smile, “but it would be excruciatingly painful.” 
  “Why?  How do you do it?”  asked Harry. 
  “Remorse,” said Hermione. “ You’ve got to really feel what you’ve done.  There’s a footnote.  Apparently the pain of it can destroy you.  I can’t see Voldemort attempting it somehow, can you?” 
(Deathly Hallows, Chapter 6, The Ghoul in Pyjamas). 

A:

Dumbledore was suspicious of Riddle from the very beginning, as per his page on the Potter Wiki:

Dumbledore was not charmed by the natural charisma and cunning of Tom
  Riddle.  In their first encounter, Dumbledore became immediately
  suspicious of his "obvious instincts for cruelty, secrecy and
  domination" and resolved to keep a close eye on him during his
  studies at the school. 

Riddle, whilst at the orphanage, had also had quite a dark past, using his magical talents to manipulate others by harming them.   This quote, however, probably indicates that Dumbledore didn't see Riddle as having passed the point of no return just here though:

Albus Dumbledore: "Did I know that I had just met the most dangerous
  Dark wizard of all-time?  No." 

(Harry Potter and the Half Blood Prince)
I would argue that Dumbledore thought that Voldemort had passed the so called 'point of no return' by 1956, the year we presume when Voldemort was denied the Defence Against the Dark Arts position:

Dumbledore, who knew of Voldemort's illicit activities since he left
  Hogwarts, denied [Voldemort's] application. 

(sourced from Dumbledore's page linked above)
The fact that Dumbledore refused Voldemort the position shows that Dumbledore was uncomfortable with the idea of Voldemort teaching and influencing young students in wizardry; he probably felt that Voldemort was a dark wizard by now.  
In the years between Dippet rejecting Riddle's application for the DADA post and when he re-applied to Dumbledore, Riddle began openly using the name 'Lord Voldemort', committed several murders, created several horcruxes.   When Riddle applied, 

Dumbledore denied him the position, suspicious of his intentions. 

(Source)
When making the application, Dumbledore had the following to say to Riddle:

Albus Dumbledore: "Rumours of your doings have reached your old
  school, Tom.  I should be sorry to believe half of them." 

(Harry Potter and the Half Blood Prince)
All of this adds up to me developing the opinion that at sometime around or a little prior to 1956, Dumbledore saw Riddle as having passed the point of redemption. 

A:

Given that Dumbledore spent years tutoring and training Harry with the specific purpose of killing Voldemort, I think it's fair to say that at that point, Dumbledore truly believed he was beyond saving.  Likewise, when Harry sees the portion of Voldemort's soul in King's Cross, Dumbledore's ghost/memory/whatever tells Harry that it is beyond their help.  The books don't give an indication of when exactly Dumbledore gave up Voldemort entirely, but they do make clear that he mistrusted him from the moment they met at the orphanage. 
As for J.K. Rowling, she's on the record saying that Voldemort was incapable of love entirely.  There wouldn't have really been a point of no return, he was always a heartless sociopath.