Panicked - is he in a Prep which finishes at 11 or a Primary? If a Prep, the Head should be advising you.
Have you received definite 'nos' from all of those schools about interview or still waiting to hear?
Have you also put in state school applications and would you be happy if these worked out?
It's unusual to get no offers if you've applied to several, but it is possible. One option is to go into a Prep for a year 7 and they will prepare for 13+ but if he hasn't met the academic standard now, you might need to be realistic that these schools aren't for him and start considering others. These could be for 11+ or 13+ and be the less selective schools.
Although the deadlines and exams have passed, it is always worth getting in touch and expressing interest anyway. It is surprising how many offers get made at some schools after the formal applications period. So if you would prefer to change at 11, don't give up, just start drawing up a list of other schools too that are a bit less selective.
Another thing you could do, is ask the schools he sat for brief feedback on his performance. Some won't be interested in giving it, but if you state that you have not been successful generally and need info to decide next steps, one or 2 might indicate what the weakness was, which could help you decide next steps.
Hopefully, you haven't had rejections by them all yet and a letter with an interview or an email is on its way.
Best of luck.