2020 and still useful, thanks wparsons!
I am another case where the key fob just started not responding. It only happened this year's winter, so I was almost sure it was the cold. I also sometimes kept the key in my jacket pocket near my chest, and it would stay warm and work 100% (not only warm up my car, but gotta warm up my keys too LOL). The moment I leave the key elsewhere it would stop working.
Then I found this thread and decided to try... I put a piece of thicker ad paper, cut to size, folded in two to double layer it, placed it underneath the battery area. I had tested it before the paper mod, and it did not work. With paper mod, it immediately worked.
UPDATE: Tried key the next morning.... it worked at first (with a slight delay) starting in the car, but then stopped working 10 mins after I arrived to destination. Took the PCB out of the key, held battery tight while mashing the buttons and nothing worked. Beginning to think it has some sort of RF interference like the other poster said.