Yes, depending on the aluminum, the heat cycle can weaken it. I've heard this from a powdercoater who does lots of motorcycle stuff. He said he generally doesn't have a problem doing them once and doesn't turn the oven all the way up, but he generally avoids coating the same wheel multiple times.
Whether it's enough to effect a frame (either the rigidity requirements of a frame), grade of aluminum, or the process used on the aluminum (billet, spun, cast, etc).... I don't know.