[AT&T Samsung Galaxy Note I717] littlewierdo:
Actually, cycling ONCE was my solution.

I was on stock unrooted with stock battery and what I noticed is that the phone VERY quickly dropped from 100% to 80% with the screen on for only about 20 minutes and taking probably 4 times as long to drop from say 40%-20%. This bugged me because I never really had an accurate representation of exactly how long my battery would last. It was also pretty weird because usually its the exact opposite, it drops slower at more full charges and faster the lower your battery. Anyways, one day I decided to drain the battery until the phone shut off, I plugged in the charger and let it recharge with the phone off and now the phone discharges evenly. By the way, contrary to what you stated, the phone will correct this over a couple of days, was simply not the case, my Note is several months old and it has been a problem day one.

It is not good to drain Lion batteries on a regular basis but the industry standard is to do it once every 3 months to allow the phone to see the general 'state' of the battery (every charge the battery will hold slightly less charge). Technically speaking however, Lion batteries like to be fully charged whenever possible. When storing (not in use for a period of longer than a week), they should be between 40-50% charged (slightly below half).

HOWEVER, all of this is a MOOT point considering most people upgrade their phone every 2 years. The proper care and feeding of Lion batteries is to make that battery last 5 years plus. Also, Android has stuff built in to shut the phone off way before the battery is discharged. As long as you dont keep turning the phone on after Android has shut down because the battery is dead, you are totally fine.

The industry standards for Lion battery care can be found at battery university's web site or in their 300+ page book.

http://batteryuniversity.com/learn/article/how_to_prolong_lithium_based_batteries

http://batteryuniversity.com/learn/article/charging_lithium_ion_batteries

http://batteryuniversity.com/learn/article/battery_calibration

Truthfully however, if you want to be rid of the battery life problems once and for all, buy an extended battery. I have a Mugen 5400 mah and holy ****, I could probably easily get 3 days out of it if I was conservative, for sure easily 2 days. Yes, it doubles the thickness of the phone and yes, the phone weighs a tad bit more and yes it is $100. BUT, if my battery is dead on my Note, my phone is useless to me until it is charged so Id rather have the added size in order to make sure my phone lasts. I dont always have access to a charger for long periods of time (sometimes 8 hours or more). The Mugen battery has the same style back case as the stock battery cover but with the added benefit of a kickstand. I also find the added size to be an improvement for me as it allows me to grip the phone without constantly hitting the volume or screen buttons.

The only other extended battery I trust is Seido, I decided to try Mugen this time around because I like their replacement case design better than Seido's.

You could also just purchase an external battery pack, itrent makes one that is 11000 mah (this is the biggest I could find) for about $75 - this little bad boy will charge the Note from 0-full 4 times, the negative being that you have a small tumor that the Note has to be plugged into for about 1-2 hours for a full charge.

Then there are additional 'OEM' batteries. These have the negative of carrying around another battery and powering down the phone in order to insert a fully charged battery. With the battery case design of the Note, **** that nonsense. I can never get the battery back open so my opinion is get an extended battery or an external battery pack.