Strange one. I've only used a few resin accessories, but have never had this problem. I normally use a light grey enamel (Humbrol) as a primer, mostly brushed on, depending on the part, and then the colour coat is also enamel (don't like acrylics), followed by the required clear coat mixed from Future and Tamiya Flat Base.
Sounds like the primer being used isn't 'keying' well onto the resin. Maybe try an ordinary enamel as a primer, ensuring the washed parts are thoroughly rinsed and dried first?