After going back and reading the original message, the only thing I can think of (other than the thermostat) is possibly an electrical surge. That would usually cause the failure to occur in the same spot. An over voltage/current would probably cause the tape to burn out around the same place. Also, when you cut the tape are you following the instructions for the type of tape you're using. Get me a close up picture of the end of the tape. That would be a picture for each side of the tape, the end that is just cut off as well as the end with the elcetrical connection.

I know, I'm a pain wanting to see the pictures, but I'm trying to troubleshoot an electrical failure from hundreds of miles away and only by looking at a few pictures and your descriptions.

Jim Smith