I was looking at my current strap this morning, and I noticed that the two contact pads that touch the skin seemed to be pulling away from the strap itself. I have another strap that seems to be in better condition. I'll give that a try, since the sensor itself has a new battery.

BTW, I was hoping someone would say it's not the strap it's the head unit, so I could justify getting a new one. You know, like how when you have a problem with shifting and somebody says "You need a new bike!"