I’ve got a radar detector and a TomTom that I (normally) stick to the windshield in my car. However, when it gets cold they like to fall off, then, once they’re off, I can’t get them to stick again. Why is this?

They do make rubber suction cups  that work in extended temperature ranges. Silicone suction cups would probably make very good suction cups for both cold and hot (and normal) conditions, though it might need some reinforcement molded in and it would definitely be expensive.