How do I keep paint nice on a cement floor?

You can't. Concrete is very porous and moisture will move through the pores damaging paint. Acid stain is the way to do it correctly. That stuff will never come off, it literally has to be removed with a grinder. Paint looks great, but isn't a permanent fix

I'm sure you can buy paint that seeps down into the concrete, staining the concrete. so scratches don't show up.

You need a sealer over the paint. Here is how other Hometalkers did it.

https://www.hometalk.com/search/posts?filter=paint%20concrete

Check YouTube for ideas: https://www.youtube.com/results?search_query=seal+a+painted+concrete+floor