We've been on AC twice in September - hot and humid, low tourist season. Consequently, a lot of places close up and wait out the area's least favored visitor - hurricanes. Likewise, some places spend the time painting and cleaning up prior to the peak winter season.
Obviously hurricanes don't hit every year, but, when they do hit, they kick butt. So, would I honeymoon in San Pedro in September, probably not, because that's the last getaway I'd want ruined by weather. If you're set on going, buy travel insurance.