Why would a car not run very well after a heavy rain?

In my experience, if your vehicle is running roughly after a rain, the problem most likely lies with moisture getting into your distributor cap. This is the cap that all of your spark plug wires run into (either 4,6, or 8, depending on how many cylinders your vehicle has). You didn't mention the age of your vehicle, but it would be unusual to see this on a newer vehicle. When the motor is good and dry, remove the distributor cap and ensure that it is totally dry and the motor is running fine. Once you've done this, replace the cap and spray the exterior of the cap liberally with a silicone spray sealant. Make sure and cover all of the top and sides. This should provide a watertight seal and prevent any moisture from entering the cap. Hope this helps.