My guesses, officially classified as S.W.A.G.:
a) Clean the battery compartment, and replace the battery with a fresh one. Analogy: An audio speaker has a resistance that may be measured by a VOM, but in use, it has impedance that varies by input frequency. Could it be that the probe does the same under actual use? If so, available current will be critical for accurate readings. And these things live in a harsh environment.
b) Cold-solder or a component is intermittent. Again, these things live in a harsh environment, and something could have worked loose. Fine when sitting nicely on a bench, not so fine in use.
c) Try the probe in a pot of water. Bring it gently to a boil. It will never get above 212F, but you should be able to follow the change in resistance as the water heats, and it should be as gradual as the heating. The difference between a test at fixed points, and a test of behavior over actual range-of-use conditions.
I would start with c) first, as it will be the most immediately revealing.
Best of luck with it!
Melrose Park, PA