I also have zipper Ariats and I love them. The zipper can get a little stuck as they get dirty but if you keep them relatively clean and WD40 the zipper every now and then they work like a charm. I have heard a lot of people that have the same problem you have, but I have heard from just as many that haven't, like myself.
Sounds like you got a dud pair. Zip ups are the ONLY paddock boots I wear! Some brands are better then others (you do want metal zippers, not the plastic kind) but they should last more then 3 rides! Dover has a great return policy so I'd give them a call and see if they can replace them. I'm pretty certain they could. If by chance they don't, you can call a shoe repair place and they can replace the zippers for you.