Q:

Studying history in an "eternal" empire

I am assuming a theocratic state as a matter of religious dogma is eternal.  It has no beginning and no end.  It has always been and always will be.  In reality of course history has simply been rewritten to omit or distort anything that might imply that there was a time the empire did not exist. 
The founders of the empire were intelligent enough to realize the empire must be capable of adapting to changes and in order to do that people must be able to learn from the past.  So study of history can't be outright banned or even restricted to a closed inner circle. 
Neither is it really practical to hide the fact other governments with different systems have existed.  Such alternate systems would be too valuable as sources of wider perspective on many issues. 
So what is hidden is the wider framework that could be used to compose long timelines and notice the imperial timeline starts after some other timelines. 
Essentially for time a modulus calendar is used.  Say this year would be the 15th year of the current century.  But there would be a number given for the century and no concept of millennia, other than noting that since the empire is eternal it must have existed for countless millennia.  People might also talk of events of the previous century.  So George Orwell wrote a book about the 84th year of the previous century.  Also allowed would be speculation and expectation of the next century.  So there would be sliding time window of few hundred years as the maximum length of historical context. 
Geographical context would be similarly localized.  A scholar might note that the heretical kingdom he is studying has familiar features, but only the most radical heretic would even suspect the kingdom was located at the location of the Imperial Capital.  And even he would simply assume there was another capital at the time, not that the kingdom existed before the empire. 
I doubt there would be major issues from this as rulers generally fail to learn from history anyway, but just in case:
How would this limit the study of history and the development of related sciences?  Would there be some practical issues?  Would there really be practical benefits over simply banning the study of history? 
Edit based on answers (or some stuff I clearly should have mentioned):
The eternal empire has no particular desire to make itself look better than it is or its alternatives worse beyond what comes naturally from self-censorship.  It is eternal.  Resistance is futile.  So the powers that be, are actually more concerned about having access to accurate information they can use to secure the future than looking good.  As a theocratic state the nominal head of state is probably the national divinity anyway.  People are welcome to go complain to him, if they think the government is messing up. 
Actually, a big part of what I'd like to know, if this kind of selective "tolerance" based on the government itself believing itself to be eternal and God ordained would be practical given that things contradicting the dogmatic stance on the empire being eternal are hidden.  That is the context for the third question concerning practical benefits above. 
Second edit:
Leushenko reminds of the vast difference between eternal and long lasting.  Quoting my comment to his answer since it explains why the empire values study of history and does not ban it or outright falsify history.  I thought that just stating they do in the question would be enough, but in retrospect that was simply wrong. 

Yes, the question assumes this difference between eternal and merely
  ancient.  Being eternal does not imply being cyclical unless you also
  assume reality to be finite in some way.  The empire rejects the idea
  of God's creation being limited in a way meaningful to mortals as
  heresy.  I imagine their view of time would be an infinitely ascending
  spiral that goes through same general pattern but never repeats.  So
  you could learn from the past, but not repeat it.  As matter of dogma
  they'd continually face entirely new events that resemble past events. 
  That is why they would value study of history. 

A:

Each year reckoning is kept in terms of the reign of the current Emperor.  So centuries are not really used, rather something is said to have happened during the year 283 of the reign of Emperor Marx Eugenes Harkonnen.  Each time a new emperor ascends, the count reckoning is restarted, with year 1 being the year starting at the last beat of midnight on the Imperial Clock in the Capital on 1st day of the month of Germinal after the ascent. 
Any and all early history is placed in an undated mythological time: "the Forgotten Times," with the understanding that all the crises of the present have happened and been successfully weathered in the past, and so the diligent will study history so that lessons may be learned.  
In the imperial histories, there is a rather tenuous reckoning going back many centuries (although heretical thinkers suggest that official histories are probably severely time inflating reign times towards the start of the continuous reckoning, i.e. Merk the Giant and the Walden and Buffetti princes might have been a mere 5 centuries ago, not the 20,000 years claimed in official histories.  All other historical documents have been purged over the centuries, starting with the great fire documented to have happened 18,000 years ago (4 centuries, suggest skeptics) that wiped out the old imperial (or not so imperial) archives.  

A:

The Empire has no problem with people studying history as long as they are using the Empire's version of it.  They will do their best (read: remove those who oppose them and burn the heretical books) to promote their version of history.  Think about it: after enough time has passed, those that had the memory of past events are dead.  The history only exist in the local folklore and history books.  But if the Empire decides to silence the historians and burn the historical books, there will be nothing left of this knowledge after 3 or 4 generations maybe.  Nothing except  the book called "History of the Empire: Form the Big Bang to the present era." 
I think this kind of government would rather try to hide the mistakes of the past than trying to learn lessons from them.  Why?  Because it gives the impression that it's perfect and cannot be wrong/ cannot make mistakes.  Therefore, the Empire has always been there and will always be because there are no alternative.  Rebels, minorities and foreign countries might be turned to ridicule to enforce this feeling of superiority.  
Well, the above is true mostly for the common people but it could be different for the elites.  In Fahrenheit 451 by Ray Bradbury, they've burned all the books but surprisingly, the elite still have access to some of them.  Or North Korea is banning American cultural products for the masses  but the Supreme Leader likes to watches movies from Hollywood. 
In your case the explanation could be that the history books always depict the Empire in a glorious way.  They tell how mediocre the other countries were and the terrible mistakes they have done.  These mistakes are in fact the Empire's mistakes but the books will say the opposite.   The Empire has always did what was right.   
The historiographers are bureaucrats in place to decide what version should be the official one.  They usually work for the "Ministry of Truth" and edit the books to keep them up to date. 

A:

Well Assuming that there are or were known to be other 'countries' much of history could be pointed to as some other country that was 'benevolently' absorbed by the empire to make life better for all.  

Would there really be practical benefits over simply banning study of history? 

For general consumption?   yes.   it is much easier to control a population that you keep ignorant.   It is distinctly possible that real history is kept for those deemed worthy, and a test to find those that could cause trouble for the empire later.   If someone starts asking questions about inconsistencies about the 'official' history they can either be indoctrinated or quietly removed, in either case a problem is eliminated. 