Mouth breathing suggests something more serious is going on: http://www.medirabbit.com/EN/Respiratory/Illness/Pneumonia/Pneumon_en.htm

Did the vet do any other tests to confirm diagnosis? Chest x-rays? In cases like this, you worry about pneumonia. If the Baytril isn’t working, a different antibiotic should be tried. In the meantime, he could possibly be made more comfortable with some humid air. A closed bathroom with a hot shower running (so the air gets humid) might work. Or if you have a humidifier for people (to use when you’re sick). You just wouldn’t put anything in it except for plain water.

If symptoms are getting worse while on Baytril, that’s a sign that Baytril is ineffective against the particular bacteria causing the infection (and therefore medication should be switched to a different antibiotic) and/or the problem is not URI-related. Baytril is not curative for all things that cause URIs, so make sure your friend lets the vet know that symptoms are getting worse and have a willingness to try a different med. My unprofessional opinion is that worsening symptoms 4 days in is enough to decide that a med isn’t effective. An antibiotic course should last, at a minimum, 14 days, but that doesn’t mean you wait until then to see whether or not it works. You should see an improvement.

Yes, you should definitely see some kind of improvement after a few days. Obviously, it takes longer for the infection to completely go away, but you should see some progress in the meantime.

Did your friend manage to get the bunny back to the vet?