Hello...I'm Dr. Coldiron and I will attempt to help you with your veterinary question! It sounds like you have some very sick birds on your hands. Birds are by nature very very good at hiding their problematic signs...they become dinner in the wild when they illustrate an illness because they become the easiest catch and are less likely to get away. The Baytril will help, but it needs to be given orally twice daily and at least once daily as an injection. This sounds like an upper respiratory condition of some type (can be viral or bacterial). Continue the antibiotics (be careful to avoid causing aspiration by giving medication to quickly by mouth), feed quality food, consider adding vitamins to the water or feed, keep warm, do not handle, etc. Your birds may make it, but once they are sick like you mentioned about all you can do is try. I've seen many become a successful case and just as many die the next day. Your vet is likely doing about all that you can with an extremely ill bird. Too much handling causes stress resulting in a decrease in the quality of the immune system.
I'm so sorry your hen is so ill. I keep hens myself and also treat them, so realize how frustrating this can be. I am very suspicious that your hens are affected by a disease called 'mycoplasmosis' and sometimes with this disease, despite treatment, then hen will not be able to fight off the infection and will still die.
You may want to ask your vet if they have an antibiotic called 'Tylan' (tylosin) which can be effective in treating this disease- for ill hens it needs to be given by injection- 2 injections given 48hrs apart. I would actually advise that you get all in contact hens on this antibiotic if possible, as mycoplasmosis is very, very contagious, and any hens that do manage to fight this off will become carriers- which would then infect any hens you try and introduce into your flock.
I hope this is helpful- sometimes despite all the treatment available its not possible to save every animal in the flock, you will always loose some, but those with stronger immune systems may well pull through ok.
Best wishes Andrea