Is there a limit to the number of times a person can get upper eyelids done in a lifetime?

As long as you are healthy physically and psychologically, as well as have realistic expectations, then there is no limit. 

You can have more than one surgery on the upper eyelids if there is sufficient skin to remove.  If you start at a young age, you may need to repeat the surgery once or twice as you age.  The mistake is to take off skin when there is not enough skin in the upper eyelid.  This can create issues with dryness and inability to close the eye.  Sometimes the skin is just crepey and a laser would be more appropriate.  And often it is the brow which is low but makes the eye area look heavy.       

It is possible to need a revision bleph especially as people age. The important consideration is being sure this isn't brow ptosis or true eyelid ptosis, both of which would be treated in other ways.