No matter if the Universe is infinite in time and space, nothing impossible can occur. Last I read, it appeared that it was impossible to create a completely convincing simulation of the Universe.
Just because the Universe is eternal doesn't mean that everything possible will happen. The Big Rip is considered possible. In the example in the article, in 22 billion years the Universe will be completely torn apart, so that no interaction between particles will be possible ever again. A lesser version might tear galaxies apart, and leave individual universe fragments that are complex enough to experience time. In that case, if a simulation needs the resources of a galaxy to create, and takes long enough to process, it could be impossible, even in an infinitely large Universe.
If the Universe is infinite, that doesn't mean that all examples of an uncountably infinite set will happen. If there's stuff that depends on exact real numbers, and we can divide the Universe into an infinite number of spacetime volumes, not everything possible can occur.
If we live in the real universe, and an exact simulation is impossible, then our experiences are limited by the laws of physics, which don't guarantee the existence of an afterlife.
Now, if we do live in a simulated Universe, and the real Universe is infinite, there's got to be a simulation where the entities like us aren't just deleted when we die, but our data structures are moved to a different environment. Assuming that our simulation wasn't programmed that way, does this count as the existence of an afterlife, when beings like us that we can't perceive have one?