That is one of the problems with acrylics, their adhesion is just not that great and they can be pulled up easily. Priming is, as you indicated, an effective way to minimize that problem. It gives something for the paint to adhere to and will help a lot..
Also, make sure your parts are clean before painting. The molding process frequently leaves some mold release oil on the sirface and that can prevent the paint from adhering. Most people just use soapy water for cleaning their parts, then allow them to dry thoroughly. I use alcohol because I'm impatient.