All rabbits have a bacteria called Pasteurella that lives in their respiratory tract. When he/she is under particular stress, Pasteurellosis can develop. This infection leads to weeping eyes, sneezing and a nasal discharge. In very rare cases this infection can be fatal (an acute attack) but I don’t think this applies to your school’s rabbit. Treatment can often be antibiotics and the removal of stress. From what you tell me, your rabbit is probably on show to a class of children for the most of the day. Especially for a shy rabbit this could be very stressful.

Perhaps your first action should be to tell the teacher about this problem and ask if the rabbit could be kept in a separate room for large parts of the day and only be wheeled out at the same time every day. This way, he will not receive any unnecessary stress or shocks. You must also have the local vet have a look at your rabbit to administer drugs which will help the discharge clear up.

Having said all of this, the problem may also simply be an allergy. See what your vet says.