To me it appears that she has been pecked around the head and face, since their are broken off feathers on her head. There may be dried secretions or food on her face and head as well. I would take a warm wet washcloth and wipe her face and head off. Put a dab of plain Neosporin or Triple Antibiotic Ointment into her eyes twice a day.
Can you show us a picture of the inside of your coop? How many roost bars do you have? How many chickens are in the coop? Can you place her on the roost after dark if she is off? You may need to spend more time with them to find out what is going on.
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I'll post a photo later, but I only have 3 hens right now. They have about 3 bars to jump up to the roosting bar, which is about 5 feet up. My boyfriend now checks on her several times after dark and once before we go to bed to put her back on the perch if she's fallen down... they have my yard to free range during the day. My boyfriend is between jobs right now, so is the one spending time with them during the day and so he sees them a lot. Just this week, he has found her on her back 3 times, two outside and once this morning in the coop. She doesn't seem to be able to right herself, but maybe she does and he just hasn't seen her. He also found her on the floor of the coop at night twice this week.
I just went out to feed them some sardines with sprinkled vitamin B and I was struck by just how scared she has become. Seems like chicken PTSD. She is very scared of Penny, the now alpha hen, but she is even somewhat afraid of her buddy Tracy (they are about the same age and from the same ranch). And although there was plenty of sardine on the plate, she would wait to see if Tracy took some first. My boyfriend mentioned yesterday that she isn't growing as much as Tracy, and no wonder, if she's even afraid to eat. That said, my boyfriend puts out 3 dishes far enough away from each other to make it harder for Penny to get them, since Penny always wants what they want... (she's turned into a real bully since she became the top girl!)
About her eyes, they seem crusty around the lids, which is what seems odd to me.... and why I thought it might be a fungus or mite... as opposed to pecking, although I think that's happening too. I'll do what you suggested.
Oh, one more thing. From the beginning, she just hasn't seemed the brightest. She can't seem to find the opening in the fence, she tries to get through the posts on the deck (which are too close together) instead of just going down the stairs to get to the garden. It was hard to train her to get into the coop at night when we first got her... Thanks.