If you're at a dock, just drop them and send them out to be professionally cleaned. Their machines do much better getting inside seams, etc. Then keep them folded and bagged until you plan to go sailing. Even in a dock locker is better than furled and rarely used. If you do leave them up on the furler, they should be wrapped very tightly and the clew should wrap twice around the sail before cleating/tailing the line. It will limit, but not prevent water from lying between the wraps.
Heck, the best solution is to get out sailing more often.