The hospital often does discharge a patient when they don't have a clear diagnosis for several reasons. One, because they've run all the tests they can think of and nothing stands out. Two, the patient doesn't have insurance (or doesn't have very good insurance), so they know they won't get paid. Three, the hospital is crowded, and they need the beds for patients they know are really sick. It's not always the best practice to follow, especially when the patient in question REALLY is ill. Not every illness shows up on standard tests, and the ones that do don't always show up the first time they're done. But, with that being said, sometimes, a patient can safely be discharged and follow up with their regular M.D.