Rotting watermelons
 

OK, I live in the southern coastal region of Virginia where it is HOT and humid. I've had many watermelons form to about softball-size only to have them rot. There are only about 3 melons that are alright on about 7 vines, in mounds, spread throughout the gardens, fairly well spaced. Those 3 are a small, seedless variety. I have one "standard" melon that was coming along beautifully, then rotted from the blossom end up. My honeydews are doing the same thing.
My muskmelons are FABULOUS! Cucumbers went nuts, then faded; various varieties of tomatoes are full and heavy to the breaking point - they need to be re-staked. Peas and beans were ok.
So, with that information, What could be wrong with my watermelons????? Thanks