Can a rabbit have allergies?

Yes. Rabbits can be allergic to any number of things from their food, to dust to their bedding. The symptoms range from runny nose, discharge around the eyes, red eyelids, fur loss, scratching, and sneezing. These symptoms are very similar to an upper respiratory problem called the "snuffles" which can quickly become deadly if not treated with antibiotics. If one sees any of these symptoms they should take the rabbit to the vet immediately.

All of that said, the problem may be allergies and the rabbit should be moved to a new location (with a sanitized cage) and if that does not help simplify the diet until food allergies can be ruled out. The vet may be able to proscribe a bunny-dosed (based on weight) allergy medication if the previous treatments did not work.