I once put together this simplistic conclusion, on the existence of reincarnation:
If you only lived once, or twice, or even a thousand times, if so, how can you live in this current, infinitely short period, in the infinite collection of past periods, if it wasn't due to the existence of reincarnation? Logically, since this period is infinitely short, due to the existence of an infinite amount of other periods, it is, in fact, impossible that you could live during this specific period, and not that you've merely lived in one long gone, if not due to the fact that you've reincarnated.
I myself do not believe you reincarnate for all eternity, even though logic tells you should. I believe you reincarnate until you find your true, fated love, and when the two of you die, you will be together for all eternity. Although logic shouldn't allow this, I'm certain the rules of logic aren't definite. This is visible in the universe, where some things break the laws of physics. Bumblebees are further proof, logic isn't always definite.