Thank you for your question. It is obvious that you love and care for your son very much.
It sounds like the treatment that he is receiving is not working well. Mental health treatment is no different than seeing any other professional; if you are not not getting what you need from one...a second opinion may be warranted.
For your part: It is important that you focus on your son's strengths. Reinforce the fact that he is seeking help...many do not and give up entirely. He has not. It is also key that you ignore those things that he does which are not helping and only reward and reinforce those behaviors that are functional. This may be hard, but to motivate someone we must start with the smallest thing and work upward.
He is also an adult male. As a man and as a therapist I know that males are notoriously stubborn about doing something that they might fail at attempting. Think about anxiety. That is a difficult thing to cope with and we often fail when we try to face our fears. For many men that is enough to stop them from trying. But, remind him that he has toughed it out this long. He is a fighter, and anxiety and depression respond to consistency. He needs encouragement, but with no backing away from the fact that he must take responsibility and continue the fight.
I cannot help but be concerned about you. You are experiencing so much caregiver stress. You can hear that you are discouraged. Have you sought out support and help? Family members of those with long term issues often suffer in silence. It would be wonderful if you sought out support for your own needs as well.
There is a skill set called MI (motivational interviewing) that has had much success in the last few years. A support group or individual therapist may be able to teach these skills to you. These abilities go beyond the scope of what can be done at Just Answer, but I do feel that you need to look at your own needs as well.
Motivate your son by reinforcement of his positives and strengths but remember to take care of you in the process. I would also suggest reading Hope and Help for your nerves by Claire Weekes. It is a good resource for both your son, and you. Also, the anxiety and phobia workbook by Edmund Bourne is excellent and inexpensive. It may give you and your son just what you need.