The car starts, then 3-5 seconds later stutters & dies. It can do this up to 5 times. So I keep revs at 2,000 until warm. It starts fine rest of day. Have 2 new batteries?
Starting problems in damp weather usually point to the ignition system. Moisture in the air can get into worn plug wires, cracks in distributor cap can let moisture in also. To test for this start the car and pop the hood, with engine running, spray water onto the suspected areas and see if engine stalls.