The elevation combined with good trail drainage design are to thank. That being said, there are a few trails at Alafia (River loop and Rock Garden) that are flatter and don't drain as well. In fact there is one section of River Loop that has had a "Closed for Monsoon Season" sign on it for a long time.
If you drive up for a weekend, you should also stop by Balm Boyette. It is only about 3 miles from Alafia (as the crow flies) and most of it drains really well too. My favorite at Balm, Ridgeline, does not and is closed most of every Summer. The 2 mile ride from the parking lot to the trail head can also get really muddy, but there is still about 16 miles of single track that drains really well there.