Time travel is easy, you see? You get send back and you receive a place and a fixed schedule for pickup. The schedule is a simple "be there every three days at 3 o'clock" or "be there every 74 hours". Doesn't matter if you're there, they scan the next hundred years for your signature in a matter of seconds. So you can come to your pickup late by 50 years, doesn't matter, you go home. Easy. Now if you're at your scheduled pickup and nothing happens, then there are only two possibilities: They don't want to get you home or they can't. So when you walk away from a pickup that did not happen, you can be sure to spend the rest of your life in whatever age you are. Easy.