Hen wants to perch all day....
- Master Enabler
Your girl is probably getting close to laying eggs (POL - point-of-lay). If so, any boys are sure to notice and are probably harassing her. This might be keeping her from getting enough to eat and drink because cockerels like to use that opportunity to jump her. Ameraucanas tend to be very mild mannered and the pullets are easily overwhelmed by over aggressive boys, so they will hide or roost out of their reach. If the other two are indeed cockerels, you need to re-home at least one of them ASAP and look for some more pullets to take the breeding pressure off your girl.
If you post pictures of them, I can help you decide if the other 2 are indeed cockerels. Try to get a good side head shot, a front head shot showing the comb, a close up of the saddle area, and a full body side shot of each bird.
There could be different things going on. Chicks go through two juvenile molts before they reach adult size. They outgrow their feathers and need to replace them. That could explain the feather loss. Molting usually doesn’t affect their behavior that much but some can be grouchier or avoid the others at this time. Each chicken can react differently.
At that age she is very low in the pecking order. She could simply be avoiding the other flock members. It’s not unusual for adolescent chickens to form their own sub-flock because they are uncomfortable around the adults. Even though they are fully integrated the older ones might still peck the immature ones if the younger invade their personal space.
She might be avoiding the two cockerels. Males normally mature faster than females. Their hormones can be running pretty wild and she is so immature she doesn’t have a clue what’s going on. At that age mating is more about dominance than fertilizing the eggs. She doesn’t know anything about fertilizing the eggs anyway at her age but she understands she does not want to be dominated. So she tries to avoid them.
Keep observing her. If she really starts to look lethargic and fluffs up her feathers so she looks miserable then she may have a problem, but from what you describe it sounds fairly normal.