There are ways to get superglue to stick to "unglueable" plastics, though. Over here in the Netherlands (and I assume other parts of Europe), Pattex used to sell a tube of superglue packaged with what was basically a marking pen with a clear liquid in it: apply the liquid to both parts, wait half a minute or so, then put superglue on one side and press together. IIRC, the liquid microscopically etches the material so that the glue has something to grip.

The Pattex brand has now been mostly replace by Loctite in a rebranding exercise from the parent company, Henkel, but the superglue-with-marker seems to be gone. Luckily I still have a couple of the pens