Trim rings will not stay on

I have a '49 Ford with the original type of stainless trim rings that go on over the stock caps. They creep off the original wheels after only a few miles of driving. It has radial tires and I'm wondering if the wheels are flexing and if so is there a way to secure the trim rings better to the wheels. The rings are in beautiful shape and I really like the look. Any help will be greatly appreciated.
 
Had the same problem with my '53 with radials. Found out the trim rings were made in China. Resolved the problem by replacing them with NOS American made trim rings...
 
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