I've been fiddling around with a game system for some time (ever since the 2010 Game Chef competition) that's based around characters that are shape-shifters. Because of this, characters have a fluid dice pool that they can move around their different Attributes so that their stats shift throughout the game. There are some limits to this, so they can't just do it at the drop of a hat, but obviously it gives even starting characters a lot of flexibility.
That said, I haven't included any mechanism for character advancement--no XP, no gaining a level, no adding another d6 to your dice pool. At this point, the dice pool acts as their health as well (I won't go into detail, since it's mostly irrelevant to the question). Given that, I don't want players to just end up with nigh-infinite health by gaining more dice throughout the game. As it stands, the best you would get as far as advancement would be that it could become easier for you to shape-shift, say you can do it faster or into a wider variety of shapes, but that would pretty much be a situational thing in-story as shape-shifting is ritualized. I really like the idea of the game being mechanically light-weight, but I might be overdoing it.
TL;DR Is an rpg still fun for more than a one-off session if there's no mechanical character advancement?