Like Patrick, I find flat black enamel difficult to remove, and purple cleaners seem to do nothing. It may help to sand some of the paint thickness away. Brake fluid is the most potent stripper in my arsenal, so I would go straight to that. Expect a long soak, and maybe pull it out every couple days to scrape the surface. That may help. Regardless of the stripper, if you are successful, don't expect clean plastic. There will be black staining, and a panel scriber will be needed to clean out the panel gaps and shut-lines and other crevices.
There is a bespoke paint stripper that is mentioned frequently on the forum, the three letter name escapes me right now. I've not used it, but according to others on here, it seems to be very potent. It's a product you brush on rather then soak in it, as soaking will ruin the plastic. Hopefully someone will chime in with the name. EDIT: The stuff I was thinking of is Testors Easy Lift Off (ELO) Also, I just read a thread on a product called QCS Stripwell that looks very promising.