Whoa Nelly. Have you tried putting in another game or messing around in the dashboard with the controller? I highly, highly doubt this is a game error. (for one, i've never seen anyone else bring up this problem on any other forum, and Fallout has been a major release, people would notice. Secondly, i've had the same problem as you before, and it ended up being the controller not the game.) Check the battery level, even replace the batteries entirely, before considering it a game error. Do you have another controller avalible you can try?
I have this issue with an entire controller, it clicks itself off the same way (replace the battery pack) all the time, it started in a single game, but ended up being a defective controller issue - the problem was constant over multiple games.