If you want to exist forever, don't worry. You do. Here's how it works.
Mathematically, space and time are the same thing. Structurally there's no difference. An object's (or person's) duration is no more or less significant than its height or width or depth.
As three-dimensional beings, we cannot perceive any more than one single instant of time. We can imagine or remember other instants, but we can't perceive them directly. However, that doesn't mean those moments aren't still there. The world doesn't turn invisible when you close your eyes. Similarly, a moment in time doesn't cease to exist just because you're not passing through that particular moment.
Spacetime is a multi-dimensional structure in which everything happens in a single moment that lasts forever. A many-dimensional creature (a god, perhaps) could look at it from outside of spacetime and see the history of the entire universe from beginning to end, and everything that happens, everywhere, all at once.
In that eternal moment, everything that has ever existed lasts forever. The only reason we see things as transitory is because we're only able to perceive three dimensions at a time. The transitory nature of things is an optical illuuuuuusion created by our three-dimensional nature. Seen from outside the universe, a being that lives forever is not much different from a being that is infinitely tall or wide.
Don't be afraid. None of us need fear nonexistence. Everything that exists, has ever existed, or will ever exist, lasts forever if you view it from outside our universe. Which means these things can actually outlive the universe itself. How's that for immortality?