Welcome to ATP, bjquat!
I really hope you don't have a limestone cave / sinkhole situation. I was going to suggest buying a truckload of topsoil or gravel to fill in the hole, but that won't help if something is dissolving your yard out from underfoot.
Maybe the county extension agent can tell you if your neighborhood is at risk, or point out some website that documents locations where things like sinkholes are likely, and what can be done about them.
http://www.pvamu.edu/cahs/coun...
http://nifa.usda.gov/partners-...
If they are 100% focused on "agriculture", they might not be excited by your problem, but I would think they SHOULD know about such issues if their county is prone to them.
After that, all I can think of is real estate agents. They probably know ALL about how to cover such a problem up so it is not immediately obvious to a purchaser. But do they know what to DO about it?
If you're lucky, a realtor will say "NO ONE in this area has sinkhole problems" ... but will they know what ELSE it could be?
Please, if you find out, let us know! That's how everyone learns.
>> It seemed to begin sometime after the May rains.
>> This depression seems to be getting slowly bigger over time.
Say, four months? Is it a few inches deep or more? Is it getting wider, deeper or both?
You mentioned "May rains". If those were much heavier than normal, maybe it was a one-time undermining that won't recur until the next unusual rainfall. But if that were the case, I would expect it to be all over local newspapers and yacked about on the Internet. Ummm ... maybe ask a clerk at a feed store? You said "Dallas-Fort Worth area", so maybe there are no nearby feed stores or farm coops.
I know NOTHING about this, but I'll speculate: if part of the issue is that water pools in the low spot, then perks down and leaches away something as it goes, maybe the cosmetic "patch it with a yard of topsoil" has some value after all. IF (if) that kept water from pooling right where the problem is worst, maybe then the REST of the yard would sink down to match the low spot. That's total, 100% uninformed speculation.
Since you didn't mention it, I assume the yard was NOT covered with a foot-deep layer of wood chips or sawdust and then topsoil layered over that. If you had, I would guess "subsidence", but have no better advice to offer than "don't do that again".
Was there any recent work in nearby yard that would change drainage or runoff patterns?
Most areas with water shortages have draconian laws about doing anything that alters water runoff patterns, with heavy fines for people touching their own land without permits and licenses. If you can find THAT department, they might be red-hot-eager to come charging out there (to hit a neighbor with huge fines or make them undo their improvments.
Whether or not they can do anything HELPFUL for anyone or suggest what might be happening underground in your yard, is a different question.