rough idle, will not stay running when it rains

Try and see where water is getting in the engine bay. Sounds like something is getting wet and shorting out. Also, if you have a sunroof, the drain might be clogged. Usually if thats happening the floor mat will get damp whenever it rains. If the drain is clogged or broken the water will run down the A pillar (along the edge of the windshield behind the plastic trim) and can cause problems with the electrical harness there.