It might be getting to much water in that area or the soil might not be draining fast enough. Mine does the same as the others stated however it’s also on it’s own. I don’t water it I don’t do anything with it other than cut it for seasoning on occasion. Love the stuff on fresh fish!
Ok here is what the thyme doctor has to say!
Pruning encourages thyme to constantly branch and put on new foliage, which keeps it compact and green. Pinch or trim back the stems at least once a month during the summer growing season. Failure to prune back may result in the stems turning woody near their base at the center of the plants, which causes them to turn brown and stop producing foliage except for near the tips. If you cut back thyme severely, avoid pruning it back by more than half its height and do not cut into the woody stem bases; otherwise it won’t produce new tender green shoots.
Although thyme is a perennial, it may last only three or four years before it naturally begins to turn brown in the center. As thyme grows, the base of the stems turns brown and woody. It produces new green growth only on the tender portions of the stem tips, so the center may develop sparse foliage and appear dead. Replacing the old plants with new ones every three years, or as needed, is the best way to avoid brown, leggy thyme.