For a rabbit to be healthy and happy, their metabolism must be in constant motion. Gastrointestinal stasis is a condition that occurs when your rabbit's digestive system stops or shuts down. This can be a life threatening condition if not seen to immediately. 

Unlike lots of animals, a rabbit's teeth never actually stop growing. As they grow, they are constantly worn down by chewing food. When their teeth overgrow they can dig into the gums and cause infection/gingivitis. This is a very common problem in rabbits but it can be prevented. 

Ear infections are very common in rabbits as their ear canals are mostly vertical. There are many causes for this common infection of the ear that can be prevented. If this infection occurs and is caught and treated early, it should not be life threatening.