We do not have enough details of your son's illness, exactly how sick he is, how far he has progressed, if he has other complications or diseases, or anything other than he is in the hospital with alcoholic hepatitis. Also, we are not doctors.
That being said, the liver does try to repair itself from injury and regenerate. It can only do this if the person refrains from injuring it further with alcohol, drugs, other toxins, etc. If your son's liver is not damaged beyond repair, his liver may be able to repair itself to some extent. Many alcoholics who stop drinking do very well for the rest of their lives. Your son will definitely have to completely stop drinking or his disease will progress.
I think it would be best to have a very detailed and comprehensive talk with your son's doctor and ask him exactly how severe your son's illness is and what his chances are for repairing his liver and recovering.
Here are a couple of web sites that might help give you some information, and, if nothing else, they can give you an overview and perhaps help you to figure out what questions you should ask the doctor. You also need to figure out how best to help your son and support him if he recovers.
http://www.mayoclinic.com/health/alcoholic-hepatitis/DS00785
http://emedicine.medscape.com/article/170539-overview
There are a couple of forums that may help you more (this is a Hepatitis C forum). The Alcoholic forum and the Addiction forum may be able to offer more information and insight than those of us on this forum can.
http://www.medhelp.org/forums/Alcoholism/show/158
http://www.medhelp.org/forums/Addiction-Alcohol-Drug-Rehab/show/1232
One thing for certain, your son must stop drinking.
I wish you and your son the very best.