I'm going to guess that the oldest plants have gotten choked out or just too old. You can get more thyme plants by layering, partially cover the plants with soil. Where the stems tough the ground, they'll put down roots. Suggest you dig out oldest plants and grass so it can rejuvenate. I would add some compost.

Unfortunately thyme plants do get old and start to brown from their center. This also depends on the type of thyme. Wooley thyme is probably the best as it is very dense and little else can get through. If you have grass growing up in your tyhme you will never be able to really dig it all out. I don't mean to sound like a pessimist but you might be faceing a do over. This type of application is often nice for a couple of year but then falls apart. Good luck!