If you use acrylics then there's a greater chance of the stuff actually curing between applications. IIRC the resin polymers in acrylic paints is what makes them great for more permanent jobs and adhesion plus they dry faster.
That's why its better to use tempera (same properties as kids fingerpaints) paints which are water based, wipes off easily and for sandies, wears off naturally. Some guys however prefer acrylic if they want a permanent weather job.
Don't know about removing acrylic from ABS if that's what you're painting, but you could try acrylic paint thinner. I heard common window cleaner works too. Test first of course.