I am also suspect about sleep apnea…. I am more so thinking the rabbit may have an upper respiratory infection that is waking the rabbit up while he’s sleeping. When my Wick had his URI, he would wake himself up frequently due to his sneezing/clogged nasal passages.
Is the vet rabbit-experienced, and did she mention anything about potential respiratory infections? Eye discharge can be a common symptom, similar to how humans get more “eye gunk” when we have stuffed noses; except with rabbits, they need medication to get over it.
It could be an allergy, as suggested above as well, leading to clogged nasal passages, which cause wheezing.
… Rabbits can also snore, but since it seems like it’s waking up your rabbit, I’m leaning more towards nasal passage clogging, and specifically what could be causing it.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.