Here is a link to two of the worst ones. These were from the other videos, so if you've already watched them, there's no point in watching this one. I'm just posting it here in case anyone wants a link to a more concisely edited video.
YouTube - Chase refusing to tap. Not cool!
Before the competition started, I overheard one of the guys in charge ask the man who later reffed it, "Hey, we need a ref; would you be willing to ref the kids?" so I'm assuming that they had a last-minute need for a ref due to someone not showing up or something. Aside from not stopping when he should have, he did a very good job, so I assume he's reffed before. He may be relatively inexperienced though, and probably wasn't planning on reffing that day. I'm glad to hear that this isn't typical though! Having never gone to a competition before, I was thinking, "wtf! Do they just let the kids break each others' arms, or what??"
I actually read some of your comments to my son, in order to prove to him that I'm not just being an over-protective parent. I think it made an impact, so thank you. I also emailed the head kids coach at our gym, and sent him a link to the video (the assistant coaches were at the event, but the main coach wasn't able to make it). He agreed completely that Chase needs to be talked to, and promised that he would. He also made the very valid point that it's not only dangerous to Chase, but also unfair to the opponent, who is then placed in a very bad situation of releasing the submission or breaking the arm (or tearing the rotator cuff, etc). Definitely a good point!
Once Chase learns a little common sense about when to tap, and once he learns some better escape technique, he'll really be able to exploit this flexibility. He's got a lot to learn though, before he's to this point.