Personally, I always wash and moisturize again, but I do not treat more than twice a day.
I would think you need to wash to get the sweat or chemicals off your face, and you will probably need to moisturize as the extra washing will dry out your face. I don't really think you need to treat again, especially if it's been a while since your last treatment. The benzoyl peroxide will work its way into your skin, so if a few hours have been transpired, I would suspect that washing doesn't affect the treatment. That's my opinion, anyway.
It's worth noting that in the Regimen FAQ, Dan says that sweating doesn't mean you need a 3rd washing
I wouldn't worry too much about this. Even if you're not leaving the treatment on your skin a full 10-12 hours before washing it off either in the shower or while swimming, the treatment still has time to be effective. I mean as long as you're not washing it off like an hour later, you should be fine. Many users report that chlorinated water even seems to help dry out their acne.
Do not cleanse and treat your skin more than twice a day. Let water be your in-between "cleanser" instead (whether the pool water or the shower), but do avoid vigorous rubbing which can irritate your skin. However, moisturizing more than twice a day is perfectly safe and highly recommended, especially after a midday swim or shower, to keep skin in balance.
Hope this was helpful! 