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Moist air can cause some real problem on the connection between the cable and the thermostat or the cable and the control module. I would clean them good as well as the pocket on the thermostat and see if that helps. Examine the end of the cable to be sure it doesn't appear damaged on the plug. Please get back to me if you need more on this and include the make and model of your thermostat so I know what we are working with. You might want to check the DC input connnections at the A/C as well. That may be loose. Those should be visible when you remove the ceiling grill for cleaning the air cleaner. Hope that proves helpful here.
Just checking back in to see if you were able to resolve this or do you still need more input from me here?