If there's moisture coming up through the concrete, then any paint will peel off of it. In the case of the paint peeling off the concrete path, then I expect the concrete is wicking up moisture from the ground, and that moisture is making it's way to the top of the concrete where it's wanting to evaporate, and forcing the paint off the surface in order to do so.
Basically, for any kind of floor you need a paint that dries to a HARD film so that dirt won't become embedded in it underfoot. Emulsion paints simply don't dry hard enough to provide good service in that situation, even those emulsions that are made for floors. The problem is that alkyd paints dry to impermeable films which won't allow moisture to evaporate out through the paint, and so alkyd paints are more prone to peeling off any substrate if that substrate gets wet.
In the case of the concrete steps, much depends on how recently after the concrete steps were poured that they were painted. New concrete is too alkaline during the first two years to use any kind of oil based paint on, and too alkaline in the first year to use anything but an acrylic paint or undercoater made especially for fresh concrete on.
My guess would be that the masonary paint that you used was meant more for walls than it was for steps. What I'd do is clean that old paint off as best you can, and paint with an alkyd or polyurethane FLOOR paint.
Keep in mind that any painted floor is extremely slippery when wet, and painting exterior steps is a law suit waiting to happen. Certainly add a traction grit to that paint to improve wet traction underfoot.
