I have not worked on this particular unit, but here is an educated guess:
I notice from the parts diagram that this unit is equipped with a 5KV DC power supply (Sears Kenmore part 6609A10003Q). If that has failed in such a way that it kicks high voltage back to the main power board, then that could cause repeated failures of the main board. I notice too that there is not that much that can fail on the main power board, so it is likely either a malfunction of the high voltage supply or the other possibility would be that the main compressor contact on the main power board is underdesigned and the run capacitor for the compressor is weak (Sears Kenmore part 0CZZA20001N), causing frequent locked rotor starts of the compressor and rapid failure of the compressor contact. It is much less likely that the compressor is hard starting for some other reason and if that is the case then the unit would not be economically repairable. Check the value of the capacitor with a capacitance meter. If the capacitor is less than 90% of the labeled value, then it must be replaced.
To narrow this down any further would require some on-site trouble shooting as Michael Karas stated. I am not usually a fan of the "parts-changer" approach to repair, but since the whole set of parts (capacitor, main power board, and high voltage supply) would be roughly $180 based on what I see on the internet, you may opt to replace all these parts together to save time and frustration. Also, the "searspartsdirect.com" website has information that shows how often the site sells each of these parts. They commonly sell the capacitor, main power board, and much less frequently the high voltage supply.
Good luck with your repair whatever you decide.