That is the trouble with plastic veneer. If you can get a panel off that is looseit will help. You have to get off the old glue in any event. Acetone will help remove it, plus razor blades. Be careful not to cut into the MDF.
The correct adhesive, is an impact adhesive. Apply to both surfaces and let it dry to the sticky stage, past the wet stage. This usually takes 20 to 40 minutes, depending on the drying conditions. Now reapply the veneer and tap with firm gentle taps with a soft hammer. You won't get it apart after that.