Vitamin B deficiency can cause this kind of imbalance. I don't know if that is it, and frankly you might never know. Pretty much every single chicken disease has some neurological/walking problem. It can be extremely difficult to figure out.
But you can buy vitamin B cheaply and put it in a ziplock, roll it with a rolling pin and sprinkle it on her food if you have her isolated. If you put it in scrambled egg alone, or scrambled egg mixed with yogurt that is good. If you don't have her isolated put brewers yeast on their food, it won't hurt any of them as vitamin B is water soluble.
We had one do this. She got bad, she acted as though drunk, would frequently tip over,there were a few days when she would just lie on her side, couldn't take many steps at all. Actually we never gave her the vitamin B. She wouldn't eat anything wet and got to the point where she wouldn't even eat scrambled eggs. I thought it might be Mareks or botulism because we had a dead toad with maggots in it in the yard. That probably wasn't it though as if they have botulism they are usually dead by the time you figure it out.
I had her isolated for awhile and she didn't improve, I finally put her back with the flock when she didn't fall over as much. She gradually got to where she was just kind of unsteady but had a pale floppy comb. I would say only in the last week, and this all happened in the summer, her comb has gotten more color, stands up straighter and her feathers don't look as ruffled. I don't know if she is laying again or not. She did stop. If you search vitamin B you'll get a ton of posts. The electrolyte mixes have a lot of vitamin B. Thiamin B 12 is the main one.
Good luck to you, I know how worrying this is. I would sit in the run with her when she was sick. She would flop her way over and always wanted to sit in my lap, but would climb up to be under my chin. I went in there just a few days ago and various chickens were coming for their pets and she jumped up and climbed up onto my chest. I think she remembers that time when she wanted hugs all the time. She used to be one of the head hens and now she is not but she is walking ok and I haven't seen her fall over for a long time but she often flies to where she wants to go. She is behind the other ones more often than not.
ETA I just read your post again. I found our hen, Amelia, on the floor of the coop in the morning one day, no idea that anything was wrong the night before. Her neck was stretched out looking up behind her. Look up wry neck and all the stuff for that too. In retrospect I don't think AMelia's neck had much to do with it.
