I think you just explained my backyard problem. Every fall there is a big center patch of grass that turns ugly brown and stays that way through most of spring, and every year that patch gets bigger and bigger. I originally thought it was a thatch problem, and every spring I've been using a special tool to remove bags and bags of thatch. But still the brown area kept increasing. It's also a low spot in the center of it, and I thought too much sitting water might be a factor. Then I decided it's just a weird type of grass that's spreading and stopped worrying about it.
But Bermuda grass fits everything perfectly. By the end of May, the brown has turn nice and green. It feels like you're walking on a dense mat of straw when over it, it's an odd sensation. It seems great at choking out weeds, I seldom see any in that section. I don't use any fertilizers or weed killers at all on the grass. Those runner it sends out are literally like wire, if you pull one section, you might end up getting well over 1' of it instead of it breaking off.
