The brake hoses from the chassis/frame to the caliper/wheel cylinder is your problem most likely...
Don't understand what problem you are talking about. The hoses are not kinked or cracked and do not leak. They were flushed out when I did the calipers. Am I missing something?
By your description, it sounds like there's an issue in the master cylinder. If you can crack a line at the reservoir (I assume it's mated to the master cylinder) and everything releases, then something in the master cylinder isn't releasing or holding pressure when it shouldn't. You can try disassembling it, cleaning everything with clean brake fluid, clearing the small orifices, etc, but most likely it'll need a rebuild kit at minimum.
Hope this is helpful.
Forgot to mention in the original post I installed a rebuild kit in the master cylinder as well when I did the calipers. Looked like it was going to be the answer but went back to the same thing after about a week. By the way, when they started locking up, I hadn't started or ridden the atv. It had just sat in the shop and every day I would go by and rock the atv back and forth to make sure it was still rolling. After about the 7th or 8th day, they had locked up again.