Older plants tend to die out in the center where the branches are oldest. When they grow, they tend to spread and this spreading makes them larger around. Lots of rain can cause problems, but because they are very mature they will probably show signs of age near the center too. Mine is just on its second year with tiny pink flowers and has not had that problem yet. Its located right next to a side of my glass greenhouse where rain will wash down exactly in that same spot where its planted. Let it grow, or try and dig up a small portiion of it and move to a better draining area. I would leave most of the plant where it is just to see if the move of a smaller part of it survives and grows elsewhere.

Ksrogers is right - thyme plants will begin to die in the centre after 3-4 years or so, while the outer parts will keep on growing. Just remove the dead bits, and they'll soon be filled in again as the newer parts spread.

Thyme can take quite a bit of water - in fact, I've never found it to be as drought resistant as most books will tell you, and I consider it quite a thirsty plant. It really only tolerates dry conditions once mature. Drainage is the important part. It won't tolerate constantly wet feet.

As mentioned, these are large expanses of creeping thyme. One is approx. 5'X 5', the other a bit smaller. The dead area of the larger one is all along one edge, although there are some other spots here and there. The other area has one large dead spot near the edge, not in the middle either. Both beds are approximately 8 years old. Thanks for your suggestions.

The dead spots can be where roots were attempting to go into soil. If there is any 'odd stuff' in that soil, or many rocks, it can reduce the roots. I would simply cut away the bad areas.

Thank you one and all for help and suggestions.