Teenagers of any species are a pain.
Teenage chicks seem to be determined to throw themselves down the gullet of any predator that happens by.
It continually astounds me how determined they seem to be to be eaten by everything. Seriously.
I do feel your frustration in that.
One of the problems I've seen with standard portable electric fences is that it can be easy for the birds to get through the holes in the fence without, apparently, setting it off. I use stepped fencing - the stuff with the graduated holes that are smaller at the bottom and gradually get larger as you go up the fence. I've found that the teenagers can't really fit through the rabbit sized fence, though they just zip on through the goat version.
You may be able to somehow shrink the size of the fencing holes by doubling it up? I guess the overlap would just short it out if it connected.
Yeah, I'll second Elena's comment. Check to make sure the fence is hot. Once you're certain it's working, you have to train the chicks to the fence. I'm not exactly sure how you go about that for chickens, but I know there are a few techniques for it. The fence can also short out if the hot wire come into contact with grass. It seems annoying, but string trimming or mowing a pathway for the fence is easier than installing something more permanent.
Make sure the chicks aren't popping over the top. Teenagers love to test their wings, so it's possible the fence is fine, but the birds are hopping out. If they are, the best thing to do is baffle them by screwing with their depth perception and making sure they can't stand on anything to hop over. You screw with their depth perception by tilting the fence to lean inward just
enough it's noticeable. It works better than you might think.
Otherwise? Maybe make an inner ring with smaller holed chicken wire. It wouldn't be for protection, but to contain the chicks so they can grow large enough to not fit through the fence. It would be a hassle to put up a slightly smaller fence inside the electric fence, but it sounds like you need some kind of something to keep the chicks from running all over the county, or at least your backyard.
I'll try to brainstorm and see what I can think up.
Best of thoughts!