Well, I tried but I can't duplicate your situation with low battery power... I found a bunch of dead AA's and paired them with other nearly dead cells... I came up with one combo where the remote won't even run, and another with slightly more voltage (but still very dead) where it will run, the LEDs are dim, and yet it still learns just fine.

The next thought is full memory, which of course it can't be since it's not learning. I'm thinking yours really is defective... with "bad" memory.