Can the hospital be sued for a patient fall resulting in brain damage?

A retired man was taken by ambulance to hospital becasue of general pain. He was told that he might have viral meningitis, thay also found bacteria in spinal cord.  After a few days at the hospital, he was feeling better and sent home.  Does not seem like a firm diagnosis was made.

He suffered a seizure the next day (he is an epileptic, but had not had a seizure in over 30 years). A family member took him to the hospital.  They went to the main desk, not the ER, and checked him back into the hospital.

Family memeber put him in a chair and went to move the car, when she returned, patient no longer in the chair and had wandered off.  They later found him in the ER because he had fallen and suffered a brain injury.  Was on a breathing tube, no longer is, but it is about 5 days after the fall and he has eyemovement, but is not oriented, cannot respond to commands, etc.

Can the hospital be held liable for the brain damges that resulted from the fall? Shouldn't he have been watched or better managed? Is this a case for a medical malpractice lawsuit?