This has happened to me, too.
I have put paint on plastic that would not dry. This happened a number of times in the past, always with One Shot enamel. Once I was given some banner material by another shop and asked to paint it and cut it up into pennants. It was two or three weeks before the paint was dry enough to allow me to cut the material without marring it. This was in the 1980s and I have not seen this problem happen for a long time.
There are a number of online forums and blogs for commercial painters where the problem of painting plastic shutters has been discussed. Painting contractors would be the true experts in this area since they paint plastic shutters frequently. The following is a blog by a commercial painter:
Tips for Painting Vinyl Shutters
Bad paint?
I expect that getting a bad batch of paint is possible, but a rarity. And the retailers that have in-house mixing stations have them set up so that even a child can operate the system. I should know, as I was practically a child when I worked at one. We did not add anything to the paint but colorants, which were either powder or liquid colors, and that was done carefully and precisely. There was a limit to the amount of colorant we were allowed to add, and we were not to add more, even if a customer insisted. Too much color degraded the integrity of the paint. Any additives, such as fungicides, dryers, dispersants, etc., were already in the mixing base. Unless a worker does not shake the paint the required amount of time, there's not much he or she can do to mess it up.
My lettering enamels that did not dry, mentioned above, were in fine condition, so the problem was elsewhere.
Incidentally, old paint may present problems, such as slow drying. Paint components tend to separate and even degrade over time. Unopened paints may even lose dryers. All paints have a shelf life, often measured in months. Most Matthews paint products, for example, including their One Shot enamels, have an unopened shelf life of 48 months, according to Matthews.
Product Shelf Life
Rather than bad paint, it is far more likely that other factors are causing adhesion or drying problems. There are both acrylic water-based paints and oil-based paints made for plastics, but not all paints will work on all plastics. Plastics vary, as alluded to by Unclebun above. Not only are there different plastics but different grades within a plastic type. Among plasticizers, for example, there are cheap ones and expensive ones, and the characteristics of the end product are affected.
Plasticizer is the term for the compound that is added to plastic in the manufacturing process that makes it flexible and stretchy. Plasticizer migrates, that is, it leaches out, over the life of the plastic, leaving the plastic brittle and stiff eventually. A plasticizer can affect the life of an applied paint film (or an applied adhesive film for that matter. This is the reason sign vinyl has a shelf life. The plasticizer gradually migrates into the adhesive, contaminating it). Because of the abundance of plasticizer present, fresh plastic may not accept paint as well as older, weathered plastic that has lost much of its plasticizer, although abrasion and a solvent wash can make a difference with adhering paint to new plastic. Krylon Fusion, made by Sherwin Williams, works so well on plastic because of the aggressive solvents it contains. It actually seems to melt vinyl sheeting a little as it bites into the surface. It overpowers the plasticizer.
The comments made by painting contractors who paint plastic shutters vary considerably. Some claim to never have problems and have been painting plastic shutters for years. Others have had failures with both water and oll based paint. I have also noticed that some experienced painters tend to use the same brands and products over and over. Maybe the ones who never have problems painting plastic shutters have simply stumbled onto a good combination.
The real answer to Marlene's question may involve the specific brands/lines of paint used on specific brand shutters.
I noted, too, a comment on one of the painter forums that some shutter retailers sell both "paintable" shutters and shutters that are not.
Of course, poor prep can always be a factor. I tend to over-prep. As a sign painter, I would use products I am familiar with. I would solvent wash first with something like Matthews Plastic Prep, or Dupont Final Klean. Then I would abrade, using red Scotchbrite on a DA sander (I have a cheapie DA at home that's electric). Scotchbrite would work well on textured plastic, as many shutters are textured. I would then do a second solvent wash after abrading, probably alcohol and water, sloshing it on liberally with a clean paintbrush and then let the panels air dry.
What paint? Primer? After the reading I have been doing in connection with this thread, I would probably fall back on the products I am used to. I would spray with Matthews Tiebond, an adhesion promoter for plastic, then topcoat with Matthews acrylic polyurethane. Expensive? Not if it avoids an early repaint.
Asking a commercial painter
What if I had no choice but to use products from the paint store? I would ask for advice, but not just from the paint store counter people. They will tell you only what they're told to say. It may be accurate. Or not. The quality of advice from paint store employees can be spotty. I would, in addition, ask two or three painting contractors what they recommend for longest life. Some commercial painters will even give you a choice. They will sometimes use one product for their "best" jobs and then a "go-to" choice for everything else. The good stuff may even carry a limited "lifetime" warranty, but cost 65 or 70 dollars a gallon instead of 35. So they buy what fits the job. The general rule among many commercial painters is that the cost of the paint is a rough guide to its performance.
Many paint manufacturers have online information on how to paint plastic shutters. These websites may be useful. But I would not hesitate to print out the advice from, say the Sherwin Williams pages about their "vinyl safe" paints, and then show it to a trusted commercial painter for his opinion.
I hope Marlene's friends are able to resolve the issue without too much expense.
Brad in Kansas City