Security System Alarm Activates in damp weather

I have a 2006 Honda Accord. The problem with this issue is it is not constant, but intermittant. When the weather is damp or it has just stopped raining when we go to use the key fob to get in the car, the car doors do not open. None of the functions on the key fob seem to work (and I have replaced the battery in the fob). Then when the car door is manually opened using the key the car alarm starts and will not shut off. At times we can correct it by closing the car door and pressing the lock button once inside the car. Once the functions of the key fob start to be recognized the alarm stops and everything works as expected. This never occurs when the weather is dry. I have had the car battery checked as a technician said the security system may be noticing a weak battery but the battery always tests ok when I get it to the service station.