There are three main problems that can result in peeling acrylic paint.
1. The surface is dirty. Usually the dirt is oil of some sort from skin, mold release, etc. Just wash the surface with soap and water then keep it clean and dry before painting
2. The surface is too glossy. Acrylic paint need some roughness or tooth on the surface to grab on to. Buffing or sanding the surface to remove any gloss takes care of this one.
3. The acrylic paint is over thinned.
Acrylic paint is made up of an acrylic polymer emulsion binder, paint pigment, a solvent (usually water, sometimes alcohol), and a small amount of conditioning chemicals (flow improver that makes the paint mixture less viscous, retarder that slows the drying, a fungicide to keep the paint from growing mold, a biocide, thickener, defoamer, etc.).
If too much thinner (water, alcohol) is added, the acrylic polymer becomes too dispersed on the surface; there is not enough acrylic polymer threads interweaving among themselves to properly grip the tooth of the surface. Using fabric as an example, good polymer dispersion looks like felt; poor dispersion looks like cheese cloth. Most acrylic paints should be thinned no more than 25% but usually 40-45% is still OK. I have found adhesion problems at 50%.
To make a thinner, more "transparent" paint mix without over thinning, stir in more pure acrylic binder by adding to the mix the paint's gloss clear (Future floor wax also is a good cheap "pure acrylic binder"). Acrylic paint gloss coat is just acrylic paint without the pigment. My current cheap airbrush paint mix is: Craft paint (like Creamcoat or Anita's), Future Floor Wax, and 70% rubbing alcohol mixed about 50:45:5. My quick mix procedure is to take 1 part paint, add 1 part Future and then add just enough rubbing alcohol to get my ideal airbrushing thickness.
Peeling paint could also result from over adding paint flow improver and/or retarder. These are available at art stores in the acrylic artist's paint section. I have experienced this problem myself but probably is not the issue here.
I have airbrushed my cheap airbrush paint mix onto the hulls of my plastic sailing ships then masked with blue painters tape and Tamiya masking tape and have not had paint peel. I have also been able to feather sand the paint edges to make repairs without peeling. I rarely prime plastic but do prime photo etch and resin.
Ultimately, the paint may need to be stripped because the remaining paint probably has the same issues.