It sounds as if you moved the lights when the bolts were a little tight. Every time this is done it removes more and more of the little plastic ridges that make the bracket stay in place.
I also have accidentally swapped the bracket parts between two different lights when working on more that one light at a time. This would do it too.
The washers will work just fine.

If you damage the bracket for the radbot, I have at least one unused bracket, maybe
even two or three.

edit- I may have brackets for the Cateyes too. I always save brackets.