I think you have to start with a completely dry windshield, otherwise the FrostGuard will freeze to the glass. If you forget or that's impossible, running the car with the de-icer on or the air turned to the windshied for defogging should help loosen it up.
I use a brush or a broom to push heavy snow off before taking off the FrostGuard. Spritzing lock de-icer on the elastics might help them unstick. And if you can think ahead and bring a big garbage bag with you when you go to the car, you can just loosely furl the FrostGuard and put it in there until you can bring it home to dry out over a shower railing, if you don't have a garage or other outside space.
All that said, you're right about big storms, they sort of overwhelm all our nifty hacks. I've found FrostGuard is ideal for the winter chore I hate the most, scraping ice off the windshield.