You know - I've heard of running the floor drains to the downspout drains, but I always wondered about getting an obstruction downstream and then having it all back up during a hard rain. A roof handles a lot of water. Am I missing something obvious? How would you keep that roof water from backing into your building?
As to the original poster - there's got to be a leak in your trap for it to dry up that fast. I know of a church addition that developed a leak in one of the waterlines under the men's bathroom. It was seeping up through a small crack in the concrete floor, and suddenly one Sunday the floor was completely dry. Upon close investigation I discovered a small hole had been drilled in the floor drain trap, allowing the seepage to go directly into the trap instead of coming up into the building first. A brilliant idea, I thought, but after we fixed the waterline leak, we had a perpetually dry floor drain trap because of that hole. I finally managed to get a sheet metal screw in the hole, but it was a bugger, and it still seemed to dry out quicker than the trap in the ladie's room. Thank God for those extendable magnets or I'd have filled the trap with dropped screws.