I take the other view, I'm afraid.....
The TV is faulty, I think.
The weak signal thing should not enter in to it. If you unplugged an antenna from a TV that was otherwise working fine, yes you would lose the picture, unless in a very strong signal area, but as soon as you plug it back in again, it should still be tuned to the right channel.
A TV should remember its frequencies, whether turned off, antenna disconnected, and whatever the signal strength.
For some reason your TV's tuner is losing its memory of its frequency settings - i.e. I think it has gone wrong.
I suspect, (if it is not under warranty), that many of these things are now getting cheap enough that buying another may be as good an option as getting it repaired, but I hope I'm wrong.