Rhinotracheitis is a herpes virus. Just like herpes in people, it keeps coming back. It is almost certainly the most common cause of chronic, non-responsive conjunctivitis in cats. It doesn't respond to any anti-bacterial agent because it isn't a bacteria. Anti-viral eye drops are available but may not be very effective, either. There is some evidence that administration of L-lysine is helpful in control of this condition. I am not sure how helpful. It can still be useful to use an anti-bacterial ophthalmic drop but the best recommendation is to use one that will work well against gram positive bacteria, which is gentamycin's weak area. A triple antibiotic drop with polymyxin and bacitracin may work better than gentamycin in this case. This is especially likely in a cat that had pneumonia because of the high probability of rhinotracheitis being involved in that, too. Unfortunately, if this is the problem, chronic non-responsive disease until the body can finally develop immunity for a while is not uncommon. Sometimes, nothing seems to aid this process.
Please see http://www.vetinfo.com/catrespir.html for more information.