IMHO, usually if water is causing a short it blows the fuse, water however that gets on the connection can cause corrosion to form which usually leads to an intermittent or complete connection failure.

Your description of high humidity in the rain from your heater leads me to believe that outside water is getting into your heater/evaporator box, causing the evaporator to freeze up, which in turn will cause the pressure switch to turn off the compressor. Locate your evaporator condensate drain hose (the one that drips water after running the A/C), gently pour some water over your A/C and heater hose connections where they enter the firewall, if water comes out the drain hose you have your culprit.