Hey -- guess what!
This thread got me thinking - so I popped open my bad keyfob to see if there was anything that can be done to it.
I found cold solder joints. One was on the component (capacitor?) being pointed at in the fuzzy pic below. The other was on one of the terminals of the battery holder. Both were very obvious - I could poke at the component with a pencil and wiggle it back & forth and the battery holder had a visible crack in the solder.
I re-flowed the solder joints and now this keyfob works at 40~50 ft again!
I guess I got lucky - quick, easy, free fix.
EDIT: The one with bad connection was the orange rectangular one in this vicinity.