Oh boy. That's a no fun! One reason this could be happening is if your phone is running a lot of apps in the background while you check Timehop. This is particularly likely if you have a lot of photos or videos in your Timehop day. If you notice your Timehop is abruptly shutting down, try closing some apps in the background and relaunching.
In any case, we get reports of every single crash. If there is a known issue, we’ll always post to Twitter with a status update. If you’re having issues and don’t see a report on Twitter, please let us know!