How to keep hubcaps on?

Radial tires apply more loads to those cheaply-made 13" wheels. They flex and either spin the wheel covers til the valve stem gets in the way, then they let go of the covers around corners. Clean the rim of the wheel cover and its mating surface of the wheel carefully, then sparingly(!) apply urethane glue (Gorilla is one brand) in a few spots around the rim. Leave it sit for a few hours, checking it periodically; the Urethane glue will bubble/foam up (which is why you don't want to use a lot). Wipe (before it sets) or trim (after) away any excess foamed glue and you should be good to go; you'll still be able to remove the covers in the normal way by prying them off.