> But why? The furnace has only been in operation since late October, and not that much---we've had a warm winter.
Remember, the pilot is on all the time, and was probably on all through the summer. The usual cause of premature thermocouple failure is an improperly adjusted pilot flame. Check the installation instructions for the furnace and see if you missed any adjustment steps. Usually the pressure needs to be checked with a manometer, and the flame needs to be adjusted so it's just big enough to set the thermocouple.