Did you ever figure out what was going on with her? Has she gotten better?
We have a hen that seems to be doing this, too. She is very inactive and just minds her own business. She will stand there and bob her head up and down (fighting the urge to fall asleep) and when she lays down, she just puts her face plants, as you said yours does. We have her quarantined now. I thought she had an illness, but starting to wonder if it is mites as the seller (we've only had her a week) said they fought off mites several month ago but that they were gone now. Maybe she still has some...I gave her a De bath, but guess I should use something stronger. I have some spray frontline, not sure if it is too harsh, I think I have some Adams spray, too, somewhere...
My hen also has diarrhea, not sure if that is a symptom of mites or not, but guess it could be if she is simply not eating enough due to the mites.