For me, the Federation should last indefinitely. It is a symbol of what Trek is about and should always be a part of the show.
As much as you say 'everything falls apart' we have never seen an entity like the Federation before. Sure it isn't perfect, but it is vastly better than anything else around it: I find it perfectly believable that it would absorb most of the galaxy given enough time.
I simply dont see it falling apart and I really dont think it should: it is a part of the Star Trek ethos and I really do not like those ideas of a Federation in turmoil or some post-Federation Trek series....Trek is supposed to be positive and the Federation is the absolute representation of that.
So after the Federation becomes this happy-perfect place, what then? Utopia is boring. Utopia leads to stagnation. How many times was that point made in TOS?
It is true that every complex human society in history has eventually collapsed... but then, it is also true that every complex human society in history was, in some manner or other, built upon the principles of inequality and oppression.
Personally, I think the Federation -- a society that has truly eliminated oppression and inequality on a scale no human society in real life ever has -- could plausibly last as long as humanoid life in the Milky Way Galaxy lasts.
And, of course, it's just as possible that the Federation may eventually peacefully persuade every other society in the galaxy to join it.... or that it may evolve into something else, something new. Maybe the Federation will encounter another interstellar liberal democracy and join with it to create a newer, larger interstellar democratic union, of which the Federation merely becomes a constituent part. Who knows?
Unless human nature changes at its most fundamental level, I think this is extremely optimistic. The lessons of history tell us that so far, every political entity falls or fundamentally changes at some point.
For example, I'm sure some of the Romans thought their Empire would last forever, but it didn't. Granted, it did last a long time - well over 2000 years (pre-Republic, Republic, Empire, and the Eastern Empire that morphed into the Byzantine Empire). But it still fell.