I have a maple chase thermostat about 20 years old. The batteries (AA) used to last about 2 years. Now only a couple months - what's wrong?

It is possible that the common wire that powers the display has been lost/disconnected somehow which would force the thermostat to operate on battery only. This could be the cause of your battery's not lasting so long. There are other possibility's but a service person would have to be On Site to test further.