Yes, mites do get washed off by a good rain, but they will be back once you get a spell of warm, dry weather. Is the curling and yellowing still getting worse?
To be honest with you, I spray my peppers weekly with the soapy water spray just as a preventative. It keeps aphids, whiteflies and mites from getting started. It's 1/2tsp. dish soap to a quart spray bottle of water, btw. Stronger isn't better, and it's pretty important to rinse the plants off if your watering system doesn't do it for you. Soap makes the leaves more sensitive to sunlight and can cause the leaves to burn in the strong sun of June.
