Max did this the first 5 or 6 times we went to the dog park. In fact he would play
fainting goat and just stop and completely lay on his side. When a dog approached he would roll onto his back. When a dog was play chasing him he would come to a dead stop mid run and then just drop to the ground and roll over. I was pretty upset about it at first but it seems that this behavior just went away. Max also used to pee or lay there until the other dog walked away. I coaxed him to get up.
I'm sorry i can't give you any more information as to why this happens. It's submissive and I certainly don't think it's a bad thing.