Bed wetting can be treated by medication, have they tried that?
Enuresis just means he wets the bed at night -- but there are medications that a doctor can prescribe that stop the bed wetting.
I would hope they would have tried some medication before just discharging him, so perhaps there are other issues that you may not be aware of?
He needs a medical evaluation to rule out everything from a bladder infection to cancer. This is a medical condition that needs first, an evaluation and second, treatment.
After all of that has been done, and if they find no medical reason, it could be a psychological issue that can be successfully treated with counseling.
With a medical and psychological clearance, he may be able to reenlist, but it would depend on how they discharge him.