Anxiety
I have a daughter with anxiety. I would suggest you get him evaluated by a psychiatrist and if necessary, be evaluated for medication. None of the suggestions we will give you will be of any use unless he can overcome his anxiety...they all involve talking to various people.
My daughter has anxiety...but she is self-aware about it. She knew she needed to get a tutor for a class...but was anxious about going to the tutoring center....so she grabbed a friend and had them go with her and that was enough to get her through it.
The anxiety may have caused issues...he didn't reach out to the grad student. He didn't reach out to the Faculty. He didn't reach out to those who would give him recommendations.
He needs to get a realistic assessment if his professors think he is graduate school material. What is his major? What is his GPA? Has he talked to professors in his major about what they think?
Did he apply to the right schools for him? Was he over shooting?
Who did he ask for recommendations? The research mentor? Others? Were they professors or adjuncts?
Did he ask them "Would you be able to provide me a strong recommendation for grad school?" or did he just hope it would be good?
Basically, he needs to talk to people who would know what may have gone wrong...his professors. This is hard with anxiety, I know. But if he wants to be in grad school he will be dealing with the same issues of sticking up for himself and reaching out to others.
He should also have a plan B...apply for jobs. He should talk to his professors on if grad school is realistic, and if it is, what to do in the mean time.