Are the PC and laptop both using the wireless connection?
If so, it could be a problem with your wireless connection. If the wireless connection drops out you'll get signed out of Messenger. It'll try to reconnect for a while (not sure how long it keeps trying for, a minute or so possibly) but then give up if it still can't find a connection. If the wireless connection then comes back up I don't think it'll then sign in automatically and you need to sign back in manually. That's my theory anyway.