Sprinkle some baking soda over the stain and rub gently with a vinegar-soaked rag. Rinse it off and see how it looks. You may have to do this a few times, Ginnie.
Good luck, Ginnie. It sounds like you're gaining on it!
Try simple green and sometimes wd 40 can work as well.
This article may help: https://cleaning.lovetoknow.com/How_to_Remove_Rust_Stains_from_Vinyl_Flooring
There is a product called Zud, that is available in hardware stores. You wet the surface and sprinkle it on and then wait a few minutes and the rust is gone. I have used it in bathtubs. For a vinyl floor, you might want to test it in a inconspicuous place first.
Whink rust remover. It's safe to use on anything, even clothes. I've used it on linoleum (and lots of other rust spots) and it worked like magic. Just pour it on and watch the rust disappear.
Hope it works for you. I'm never without that magical Whink. ;)