There are many possible reasons for a rabbit to dribble urine and/or sit in urine, and the only way to know for sure is have your rabbit completely examined by a veterinarian experienced in rabbit medicine.
Ask for references, credentials concerning the latest in rabbit medicine, and last but not least, the subject many of us sometimes do not want to discuss — euthanasia.
Most veterinarians who are really interested in rabbits are excited to have the chance to do bloodwork and urinalyses, because with each result their own knowledge about rabbit medicine increases.