If we talk about some forum contests, it seems to me that the winner keeps the badges permanently, and the others get them temporarily, while for some other badges the status is permanent.

@gmaxwell has a badge called "Bitcoin expert" and there is no doubt that it is something permanent, although I have to admit that @achow101 seems to have had a badge in the past that I can't see now (Bitcoin-Qt core developer). It is possible that (like some other things) badges can be removed on request.