I would be more than a bit annoyed w/ that P.A., my P.A. is a pain but yours i have to say is worse.
Sounds like you got your answers. I had very similar problems. When i first got my rechargeable i had difficulty making a good charging connection. as time went on it got a lot easier. maybe it was everything settling down, maybe i got better at positioning it. or both??? Also, the remotes suck batteries like crazy! I always swap out the batteries when i have difficulty programming and that usually fixes the issue. Not sure if that was your problem but 4 weeks is about all i get w/ my remote batteries.
anyway, good luck w/ your cold