I think it is important to remember that the immortality mentioned here is a protection from biological causes of death, but there are plenty of other obstacles to prolonged existence (especially prolonged self-consciousness and memory, which is harder to wrap one's head around).
Take the popular theories of the universe's lifespan (or life cycle).
1) The universe is expanding exponentially: eventually every star will die and there will be nothing to birth new stars. The universe will stop moving and hit a zero Kelvin freeze.
2) The universe cycles between big bangs and big crunches: information cannot survive through a crunch. Well maybe one binary bit? hehe.
3) Some sort of multi-universe collisions or string theory madness: who knows but there could be some event that wipes out what we know as reality.
Basically, I am trying to point out that immortality is probably a fundamentally flawed concept. A simpler approach might be to consider memory. Memory storage cannot grow forever (let alone be accessed efficiently enough) and while we could cap memory and still exist indefinitely, I think we would have to hit a ceiling of knowledge attainment and we would just be spinning a wheels like a more exciting version of a rock (not that humanity is any less of a _process_ right now).
Smarter people than I have already dwelled upon these issues and probably have better answers than mine (esp. since I have no answer). Asimov's "The Last Question" is an interesting short story that covers this area a bit.