When you paint something which has already been painted, sometimes the solvents in your new paint interact with the old paint on the surface, with somewhat unpredictable results. Generally, the results include lifting in the form of either wrinkling or peeling. This is very common in auto paints, and in anything that comes out of a spray can. But I've found a set of solutions for dealing with paint interaction which are fairly effective when combined.
For example, when painting a car which has been repainted multiple times, one standard way to handle the situation is to spray the entire vehicle with a coat of polyurethane primer. The polyurethane forms a layer which paints won't reach through in order to interact with lower coats. However, the primer itself may interact with paint layers. This is also extremely likely when dealing with a part which has been sprayed from a "rattle can", or a typical spray can. These paints are usually poorly labeled and it's often not clear if you're getting a urethane, polyurethane, or even a lacquer.
The fix I've found is to use a water-based midcoat to reduce paint interactions. I'm using Citadel Colours white primer, which is actually formulated for spraying lead, pewter, and plastic miniatures used for gaming — it's sold by Games Workshop which makes Warhammer. This paint does not interact or interacts only minimally with paints which react readily with other coatings. If you spray it on "dry", meaning fast motions and/or from a relatively long distance, it hardly has any ability to interact whatsoever. Using this as a midcoat can help you get over a bad interaction.
The other solution, which I learned in Frank Katanic's auto body class at Yuba College in Marysville, is to wet sand with solvent. In class we learned to use wax and grease remover, but if you don't have that you can use good old isopropyl alcohol. The surface must be dry, but the paint does not need to have actually cured. Put on some nitrile gloves, tear a small piece of 500 grit and wet it with a few drips of alcohol. Paint will close (clog) the paper fairly readily, but it opens easily when wet with the solvent and as you handle it, so just keep wetting the paper with a few new drips and rotating it around so that you're sanding with an open section. Normally you have to wait for the paint to cure (at least partially) before you can wet sand, which is a real problem for paints with an up-to-30-day cure time. When the paint interacts in spite of your best efforts, use this technique on the raised parts, then go back over them with paint. The dryer you spray it, the less it will interact but the less of a bond it will form with the prior layer of paint.
Obviously, you can also remove the interacting paint with paint stripper. Use a gel-type stripper to avoid runs, and mask off the part of the body below the area you are stripping. In general, the nastier the stripper, the faster it works; "AIRCRAFT remover" is horrible stuff, but it works like lightning. Gentler options like Citristrip are effective but slower and may require the use of more product. Once you are done, feather-edge the paint with 180 grit on a D.A. sander to avoid leaving pattern scratches, then smooth with 500 grit wet sanding before painting, treating any exposed metal with Metal-Prep or a similar etchant which does not leave behind residue. The problem with using this approach to solving paint interaction is that you will create bulls-eye rings which tend to react in a circular pattern. The best approaches are therefore to either take the entire panel down to metal, or to simply bury the reaction with a paint which does not react with either the basecoat or topcoat.