[dmsfrr]

I'm not sure I understand your question.

The smaller hub caps, full wheel covers?
Some full wheel covers do lose their grip over time and fly off when cornering.
Bending the tabs on the back side for a tighter fit may take care of it.
I've seen other folks comment that wheels made before the mid 60's flex more than newer versions and that could be part of the problem.

The tread on the tire?
Tires do age-out.
Most tire shops won't service one over about 8 yrs old, due to failures and legal liability.