Hmm....does she seem to 'groom' herself lot? It is known to happen that they want to strip themselves for some unknown reason.
Dropping feathers other than for usual moult indicate that she is under stress for some reason. Perharps she is not getting everything she needs from her diet...perharps is something else, but when feathers start dropping..her body is not able to keep them going and they have to go to keep rest of her system alive.
Cider vinegar in drinking water doesn't hurt though I doubt it will be the remedy..the way cider vinegar works is that it makes conditions inside better for those 'friendly bacteria'..thus she is able to utilize any nutrients better from her diet.
Without actually seeing your bird it is difficult to say what is the reason, if you say she is free from mites and lice
and has been wormed, next step would be giving her some supplements. 'Poultry drink' is vitamin and mineral supplement that would not go a miss.....make sure your pellets are 'fresh' and not kept too long...'growers pellets' would be good idea mixed with the 'layers pellets' as it is not necessary to encourage her to carry on laying while she is not in condition for it. It is not easy to provide her own choice of feed when there is others around so compromise of mixing the feeds won't affect others performance.
Make sure that there is plenty of grit available and perharps giving you girls fresh 'dust bath' source ensure that they are keeping themselves groomed. You can make nice and healing 'dust mix' with dry sand, wood ash and some diatomaceous earth (if you are not familiar with the last one, google it and you get some brand names for it)..the last one you can use to dust whole of the coop and nest boxes to deal with the parasites. I buy it from ebay under 'diatomaceous earth' name rather than brand name and it is MUCH cheaper that way.
If you have access for some nice berries..like currants...those would give some good vitamins that will add into their diet...some greens too..plenty of variety. You could hold off from corn as it is just energy food and not much 'goodness'. Some protein will help with feather growing (good during moult) with could be crushed up snails, worms or some dog food .. 'loaf' sort in tin ,but keep off from poultry varieties or cheaper option is 'complete' dog biscuits that are soaked soft in hot water. I give some for my girls every now and then as they don't get to free range and have access that many 'meaty bugs', but particularly during moult is when they truly need it and it helps them get over the hassle very quickly. I don't think layers pellets are that 'complete' food anyway and some complimentary 'bits and bobs' does good for them.
All advise I can give is really based for checking that all the basics in poultry care are in place....lets hope it is 'just' matter of adjusting her nutrient uptake and nothing more serious.
If you girls are 'getting on'..when they get older they can come up with all sorts of troubles...why farmers don't want to keep hens going on for long.
Other than that....get the knitting needles out and make her a jumper for the winter
