Thanks for the great suggestions. I hadn't thought about liquids dripping down the wire, but I'll bet that's part of the problem. And the alcohol wipes sound like a winner also.
As an update, I heated up both of the probes today to nearly 500 degrees and was surprised to see liquid boiling out the ends of the probes. After heating them up for about 15 minutes, I let them cool down, and surprise, they appear to be working again. I thought that might helps others having problems.
Again, what a great forum!