DS applied for well over 20, possibly closer to 30. He got a few no's, a lot of interviews but got turned down at a lot different stages - resilience is definitely required! I always said to him even if he got nothing this is an excellent demonstration of just how difficult it is to get a job - and how you will need to make sure at university that you stand out from the crowd. That means a lot of impressive extra curriculars beyond your course - you can't just come out with a 2:1 and think you'll walk into a job, you have to stand out.
I made sure during Yr 12/13 that ds got involved in relevant volunteering and joined relevant school clubs. He also did a lot of MOOCs, Youtube tutorials. designed his own stuff, made his own websites of his interests etc all relevant to what he wanted to do. This was all important to show a real interest in his subject I think. Also be clear why you want to join that company - how your ethics align with the companies ethics. You need to have researched them well.
At interview, for the really highly sought after apprenticeships we found that many of the applicants were very confident, polished, likely to be used to public speaking, private school applicants. We could tell as they were all in their posh school blazers, turning up in their parents very expensive cars. DS didn't really stand much chance bless him!
He found at interview that be able to talk about working as part of a team almost always came up, times he overcame a problem and times he demonstrated x, y or z. He always preferred interviews where he had the opportunity to demonstrate his skills though rather than just personality type and those were where he did far better. He certainly found though that coming up with a lot of different possible questions and thinking about/writing how you'd answer them helped and the more interviews he did the more used to doing them he got (and better at them).
Have you looked at DS's CV and cover letters/question answers? Is he using a template and have an impressive looking CV? I would recommend looking it all over and giving him some hints and tips on how to play everything up and draw attention to him being a hard worker, team player, self starter etc. Kids often aren't used to writing in such a formal way and drawing out the skills they've learned or demonstrated from what they've done. Make it all as professional as possible.
DS got his apprenticeship around 7 months after he first started applying and absolutely loves it. So don't give up! Apply to loads, be prepared to move (ds is in a shared house) and give him as much help as you can.