Most people buy MGA interior panel kits complete, some make their own from scratch, but likely everyone will had the same problem. Where the vinyl cover is folded over the panel edge to be glued in back, fairly often the material needs to be cut with fingers to follow around corners or curves. These vinyl fingers may not lay down flat, may want to pop up, or the glue may come loose with time. The loose fingers can be quite a problem.
Here is a photo and tip from Mitchell Andrus in Mills River, NC, USA who wrote:
"This is what I do inside Moss's door panels. A scrap of vinyl super-glued to the rear. This keeps those relief fingers stuck down".

Additionally there may be a problem with the vinyl material itself.
"In almost all roll vinyl there is a cloth backing upon which the vinyl is applied during manufacture. The cloth adds strength and allows one to adhere the vinyl with adhesives such as contact and landau cements. Cheaper roll vinyl has a cheaper cloth backing. If you look at the back of the vinyl you can see that the cloth is almost completely absorbed into the vinyl layer. This is bad news if the vinyl is to be glued down, because the compounds in the vinyl that keep it soft and pliable migrate to the surface. These compounds soften the adhesive and cause failure, in most cases only a year or two. In other words, the cheap vinyl used is not correct for this application. They should be using a vinyl with a more substantial cloth backing".