When I first got Eve I knew she was going to get a URI. She was on antibiotics for almost a month. Then when I stopped it came back. In total it took 3 months for her to get better. I have seen a couple of kittens grow into adulthood never getting better and constantly on meds.
It is possible that it could be viral, as Jade said. One virus looks very much like an URI and really irritates the eyes as well. This is a herpes type virus that humans CANNOT, I repeat, CANNOT contract. Believe me that was the first thing I asked the vet and with all the snuggling I do I would have gotten something by now. You can try adding some Lysine (an amino acid found in vitamin sections or health food stores). Look for the powder filled capsules and mix it in with a little bit of wet food. I would give her about 1/2 a capsule. If its not affecting the eyes than it is probably some thing different. Just make sure she eats and drinks. I have seen cats practically starve themselves due to URI's and we have to force feed them. I think they do it on purpose becuase they know they get the good stuff then.