A risky strategy that could work is to call UA a few hrs before departure and explain that you have a flat tire / dog is sick / someone broke into your house etc etc and that you probably won't be able to make the flight. I don't have experience with UA, but other airlines will usually re-accommodate you for free on to the next available flight, in the OP's case, I assume this would be the next day. [I am not condoning this method, but merely offering it as a suggestion - personally I'd just suck it up and pay the change fee.] The good thing about discounted fares is that, even if you have to make a change (and assuming there is availability,) the most you would lose is the change fee because you are 'upgrading' to the fully flexible ticket that you would have paid for from the start.

Cheers,