I did some more searching yesterday, and came across a post on another forum about a similar problem. This guy had washed both the electrodes on the Wear Link, and scrubbed the connections (the "buttons" on each side of the transmitter). So I washed the electrodes with dish soap, and used both soap and the dish brush to get into the connections.

I went skiing again this morning, and it worked!

A couple of other things I picked up:
  1. Change of battery might help, even if the difference in new and old was only 0.33V.
  2. Some jerseys are more staticy than others, and might cause problems with static electricity.