Why proteinase K doesn't degrade itself?
According to invitrogen proteinase K does undergo autolysis, but that some leftover fragments still have protease activity. The solution should be stored at -20C, this low temperature is probably the best way to prevent autolysis. If you're using the enzyme to digest protein at 37C, you'll just have to deal with losing the proteinase k during the reaction and make sure you add enough to destroy the target protein before the proteinase is depleted.