HotRod:
You may be a candidate to try this single/double wire electric fence option:
http://www.plamondon.com/faq_electric_fencing.html
Robert is a BYC member and sometimes poster. As I understand it, the single / double wire fence option works best when the acreage available to the birds is larger.........an acre or more. That way you have enough range area to satisfy the birds, so they are not likely to fly over it, and they too will learn to respect the fence and not punch through it as they do the fence you have now. So they stay in and predators stay out. I currently have such a fence setup, but mine is currently being used to keep raccoons out of a patch of sweet corn. So far it is holding. So far, my 8 week old pullets have not ventured out that far to test it, but it is waiting on them to try.
Option B is to purchase electric poultry netting, which in one iteration, comes in a length of around 160 feet. That would be 40 feet square or some such configuration. That creates a smaller area at a greater cost, but is what a lot of people are using. Sources include Premier 1 in Iowa and Kencove. Both are online.
Not sure what fencer you purchased, but fencers are not created equal. You want one with enough zap to it that nothing on the inside or nothing on the outside will risk getting zapped over whatever it is on the other side. The risk of getting another jolt that will loosen their teeth and set their feet on fire is is simply not worth it, so they learn to respect that fence. Part of that is the fencer and part of it is setting it up right, getting a good ground being a critical part of the setup.