Life, as we know it, requires an energy gradient (i.e. a way to do usable work).

The currently most likely, theorized end-of-universe scenario doesn't have that ("Heat death").

The...erm...more 'exciting' end-of-universe scenarios (Big rip, Big crunch, Big bounce, False vacuum decay, ....) are even more certain to end any life that managed to hang around until then.

But, hey, we don't know everything about the universe yet. So there may be ways of sidestepping the problem.