Common causes are foreign object in the eye (often piece of hay), dental problems, plugged up tear ducts or an eye infection. How old is your rabbit? Is there redness in the eye?

Given his age and the fact that this has been going on for a month, this could be related to his teeth. Teeth problems are common in rabbits, especially as they age. A vet would have to exam his mouth. Treatment as a rule consists of a dental burr to shorten and even out the teeth.

Hopefully this isnt the case with your bun, but whatever it is, a vet needs take a look. A vet can prescribe antibiotic eye drops.

Since vet services are currently not as readily available as in normal times, there are some things you  an do at home while waiting for a vet appointment. First of all, I’d try rinse the eye with normal saline. Saline eye wash for humans is good.

If the problem persists, you can do a warm compress on his eye. Chamomile tea is good for this. It does require the bun to be still for several minutes, so it’s best if you can sit him in your lap for the procedure.

First make chamomile tea, let it steep for like 10 minutes. Let it cool til luke warm. Wash your hands thoroughly, then soak a clean compress in the tea, and squeeze out excess fluid. Put the wet compress over your bun’s eye and the area towards the nose. This can help unplug or widen the tearduct. Keep the compress on the eye for several minutes. This is often pleasant for the bun, but if your bun is very skittish, he might still protest, of course. Covering his other eye with your hand can sometimes help,  rabbits are a bit like horses in that respect.

Repeat the warm compress treatment daily, unless he really hates it. You may see more goop right after the treatment, just wipe that off with a clean compress. Be very careful not to touch the other eye with anything that has been in contact with the affected eye.