I've painted concrete a lot in my days. However, as you've seen, the problem is that when paint gets when, it's slippery to walk on. That's why it's best to only paint walls. You see, you don't walk on your walls. If you could, you'd slip a lot.
You're living in a Danger Zone. I hope your liability insurance is current. If anyone was to hurt themselves on your painted walkways and steps, you could be in for a serious lawsuit! You can continue to paint your walkways but you need to find a paint that has SAND in it. The sand is a non-slip additive to the paint. You *must* constantly keep stirring the paint because if you don't the sand will settle out on the bottom of the can. Maybe you need to have some help when you do this job. You paint and someone else constantly stirs. That's the *perfect* scenario to catch up on all the neighborhood chat.
Since you said it's always getting dirty, perhaps you can build a canopy, of sorts, over top of your walkways and steps, then enclose it. This way, they won't get wet *and* dirt won't collect on it. At worst you'll only have to dust the floor! If you *really* want to solve your *ugly and slipping problem*, get rid of the paint.
The only pointer I have for is to *point* out to everyone why it's a bad idea to paint cement walkways and steps. As one can see, this is a potential liability problem. Perhaps our resident Attorney can share with you the *downside* of continuing doing what you're doing, from a legal perspective of course! Have a nice day!