If we know one thing about time travel from watching cable, it's that given the opportunity, someone will always travel back in time change things, whether to prevent World War II, or start World War III, or save Lois Lane from an unpleasant death. Whenever this takes place, we end up with a different timeline, presumably one in which someone different decides to kill someone's parents before they're born or whatnot, which creates yet another timeline, which is wiped out by someone else's temporal shenanigans, and so on like a four-dimensional Escher painting.
How many times does this take place? It's impossible to say. As each timeline is created it's instantly replaced, and you can't get a thing done without finding out that your brother is suddenly your aunt, and rather than being a VCR repairman you're Squindar, Lord of the Under-realm. It is for measurements such as these that the word "bazillion" was created.
The only way reality can exist for more than an instant is when someone, by accident or design, changes things to create a universe where time travel is never discovered. And that, my friends, is where we are now. Time travel may be possible, but anyone who tries to discover it will fail, probably due to a misadventure of ludicrous improbability.