GFCI is popping for no reason
You say that after the rain and some period of drying the GFCI returned to normal working condition. Indicates your problem is "outside" related or influenced. Take a real good look around the outside of your building. Look for any plugs that may be catching moisture from above as the rain comes angling in.

Often as an electrician I come across previous wiring in homes where they jumped the inside GFCI to outside plugs to save money on spec homes. Home owners complain that outside plugs are not working yet breakers are un-tripped. I always say go look for a GFCI in one of the bathrooms, if it is tripped then reset it. 

So if you have a non-contact tester you could turn off the breaker that supplies the inside GFCI, and test to see if any plugs on the outside of house are off. If so, make sure that any waterproof covers are in good state and replace them if they appear to be in poor state. If you have a cord plugged in for any length of time you should have a "in-use cover" installed.

Even a small amount of moisture leaking over the receptacle will cause small current leaks to neutral and therefore trip the GFCI and you will not be able to reset it till it is dry. Also any foreign materials will exacerbate the situation. So surfaces should be dry and clean on the receptacle.