Isn't suicide always an option? When it comes to imagining immortality, I'm like Han Solo, but limits are conceivable and boredom might become insurmountable.
The real question is whether intelligence has a ceiling at all - if not, then even millions of years wouldn't be a problem.
Charlie Brooker's Black Mirror tv show played with the punishment idea - a mind uploaded to cube experiencing subjectively hundreds of years in a virtual kitchen with a virtual garden, as punishment for murder (the murder was committed in the kitchen). In real time, the cube is just left on casually overnight by the "gaoler" for amusement. Hellish scenario.
(In another episode- or it might be the same one? - a version of the same kind of "punishment" - except just a featureless white space for a few years - is also used to "tame" a copy of a person's mind that's trained to be a boring virtual assistant for the person.)
Isn't suicide always an option?
Not if you're an upload.
http://www.theatlantic.com/technology/archive/2015/05/immortal-but-damned-to-hell-on-earth/394160/
With such long periods of time in play (if we succeed), the improbable hellish scenarios which might befall us become increasingly probable.
With the probability of death never quite reaching 0, despite advanced science, death might yet be inevitable.
But the same applies also to a hellish life in the meanwhile. And the longer the life, the more likely the survivors will envy the dead. Is there any safety in this universe? What's the best we can do?