Times like these is when filling the chlorinator with tablets isn't a bad idea, IMO. It will help maintain the FC while replacing CYA lost to rain (CYA doesn't evaporate, but if you are getting 5 inches in a day you are losing water to drainage, which does reduce the CYA). You will still need to test regularly and dose with liquid chlorine if necessary, but it can help you to stay on top of things. Be especially sure, if you do this, to watch the pH and TA as the pucks are acidic.
Once the monsoon has passed and your CYA level is where you want it you can transition back to strictly liquid chlorine mode.