In my garden it's grows through the winter and sets seed only in the spring. It self seeds in my garden annual and doesn't even sprout until the cooler weather of fall. I'm also in central Texas so I'd expect similar timing.
Considering it does so well in my garden, I can't say what problems it may have. That's actually why I hadn't chimed in. I'm at the base of the hill country where the soils start shifting to pure caliche.
If it is an issue of drainage, it's not to late to replace dill. Mix organic matter (
compost or aged manure is perfect for this purpose) at least six inches deep into the soil. Use
enough to raise the bed surface by at least a few inches. Then either spread fresh seed or transplant seedlings into the bed. The plants will remain small over the winter (you may want to cover during freezes) but as soon as the weather starts to warm in the spring they'll rocket up.
Don't forget to mulch as the plants grow. If you can maintain a good layer of mulch, it will protect and
feed the soil biology. That is what will develop a good soil structure in the future. Just mulching alone can completely change a
garden bed over time. Ideally you only need to dig a well mulched garden when harvesting
roots.