Hawking tells us that if time travel were possible someone from the future would have come back by now. Time is fragile. It is so fragile that whenever anyone from the future does succeed in going back in time all of history from that moment forward is erased. As soon as the time traveler sets foot in the past he ceases to exist. He’s never been born. If he has never been born, however, he can no longer go back in time. And as soon as a history exists in which he does not go back in time, all history is restored. Does this create an infinite loop? Not from the point of view of the time traveler. The forward pressures of time are such that though this all takes place in a millisecond, at the expiration of that millisecond he is already past the time wherein he returned to the past. His only experience is that he has failed. He is still inside his time machine, and he is still in the present. And it does not matter how often he does this. Thinking he has failed, he may build and rebuild his machine. Whenever it works it will seem to have failed, because time is self-correcting. The moment of return and restoration is marked by a pause in memory, the forgetting and remembering of a word.
What happens to all those new histories? Nothing is lost. Each of those trips to the past creates a branch that continues, diverges from the restored time, growing forever in a new direction.