Trim rings will not stay on

[Bruce Compton, Canada]

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.