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?
I think you have totally misinterpreted the point made in TOS. NONE of those societies were true Utopias. They were fictional, often computer controlled [and imposed] prisons under the guise of Utopia. The Federation is nothing like that and I think you should perhaps rewatch a few of those episodes.
A true Utopia would not lead to stagnation. Hypothetically, with everyone able to pursue their own interests and better themselves unmolested, the potential for improvement and advancement is limitless.
I actually only see the Federation continuing to absorb everything else around it. To be frank, I think this is one of the underlying themes of the whole franchise [that many people miss]: that all the 'bad guys' with their Authoritarian, militaristic states see the universal appeal of the Federation. At its core, its ideals appeal to all, it is simply a matter of time before the peoples of neighbouring states realize that.