Welcome to the forums and thanks for being here. I really appreciate you reaching out trying to get some help for your son; it sounds like you're a great advocate for him.
It's hard to get an idea of your son from one post, but the fact that he's attended rehab several times and tried a number of antidepressants shows me that in a sense he is (or was) committed to change.
How do you feel like your son is coping now? Is he still interested in change? Is he seeing a therapist at all?
Personally I feel like some medications and rehab centres can be a little bit of a cover - they might look at reducing alcohol intake but if they can't get to the core of why your son copes with alcohol, it's going to make it so much harder to stop.
While I'm not familiar with the long-term rehab centres or LifeSkills, I can recommend this resource. If you haven't tried them already they might be able to give you an idea of the next best step -
If you scroll down the bottom of the page you'll see the ADIS (Alcohol and Drug Information Services) and the phone number for your state. They do both intake, advice, assessment and referral so hopefully will be helpful to you.
Hope this helps,