Well, you are trying what I was going to suggest, using abrasive string to polish up the eyelets and the tuning pins (you may also want to go over the bridge pins as well). There very well could be rough spots that you can’t see or easily feel inside the eyelets or string holes, so that is the best first step.
Other than that the only thing that I can think of that would be causing such a problem (assuming that you simply haven’t been having very weird, varying, frequent weather changes) is that maybe you have the strings tuned too tense? Make certain you are tuning them to the correct octave.
I did talk to the owner before me who told me that in the 15 years he has had it there have been only a few strings break that they have had to replace. Granted it didn’t get played or tuned after the new string was on so the tension was not as high as I have it keeping tune.