Superglue works well, and my experience is the same as some above - many of the super-cheap types like you find in a Pound/Euro shop are fine (literally as good or better than name-brand stuff). The type I'm using at the moment also has the best shelf life I can remember for superglue in a tube, and that's with the humidity here regularly topping 85% these days. This indicates the cap fits a heck of a lot better than the Loctite one!
Anyone who wants to go the solvent route, one thing to try is a strong liquid paint stripper or brush cleaner/conditioner, e.g. Rustin's brush restorer; these can contain one or more solvents that dissolve many harder plastics like styrene. Something like this is likely to be waaaay cheaper than any commercial plastic glue.
Einion