If time is infinite then theoretically every eventuality will occur an
infinite number of times. Therefore, at some point we will all be
reincarnated in every possible form that can carry on our conscious mind.
However, there is likely to be a very large amount of time between death and
resurrection, unless we are in control of the process (cryonics).
For a rerun to occur (a being that develops so similar to yourself it carries
on your consciousness) the surrounding world would have to be exact in every
detail up to the point of your death (so that the being has the same memories
and 'thinks' it is you). For transhumans this seems pointless as you gain
nothing from it, it does hold one interesting point to all those looking
forward to an afterlife. They will live, but they won't know they've died.
Simulation as a posthumans recollection of the past, or as an experiment
could also rerun dead minds. After simulating the consciousness of our
chosen victim, we could then put them into a steady state of evolution to
become fellow posthumans.
Preserving yourself at the time of death gives you a smaller time frame in
which to be reincarnated and would hopefully mean you'd have someone around
to tell you what happened.
Not dying in the first place seems like a good idea, but whatever happens
you're not going to die. However, you might be resurrected in the year
98,000,023, be reincarnated in a mirror universe (not that you would know) or
be subjected to some nasty multiple consciousness paradoxes.
In short, even if we are all immortal, it's better to be in control of your
own resurrection (especially if time turns out to be finite, in which case
we're all screwed).