Cyanoacrylate is a rather strange beast. It gets used for a lot of things where it's not really the best stuff - and often works well enough. There are quite a few "plastics," though, where it just doesn't do a very good job.

It is kept liquid by oxygen from the air, and as long as it's exposed to air, it won't set. The theory is that when you clamp it between two surfaces, so that air can't continue to get to it, it will harden; but in order for it to set up, something has to absorb the oxygen that's already dissolved in the glue. Most metal surfaces will absorb (or adsorb) enough to set it up. A few (cadmium - as in the plating on lots of parts) won't. Most plastics won't do a very good job.

If your crazy glue sets up at all when you use it on many plastics, it's only because the surface wasn't clean - and the crud sucked up the oxygen. Unfortunately, then you've got glue stuck to crud - but the joint strength depends on how well the crud sticks to the parts, which is not usually very reliable.

If you clean the joint well enough for the glue to actually "attach" to the surface of the parts, the surface of most plastic is insufficiently active to fully polymerize the glue - so it "stiffens," but doesn't really get hard. And that doesn't work very well...

The "crazy glue" grades of cyanoacrylate don't ofen come with it, but if you switch to the "Loctite" kind, you can get a primer intended to solve the problem. The primer is intended to get all the crud off, and in addition leaves a trace coating of colloidal metal, usually silver, to act as a curing agent for the "glue" by absorbing enough oxygen to set it up. You never wipe the primer off. You let it drip off, and then evaporate to leave the active material in place before you apply the glue.

In principal, an epoxy should bond to most plastics, but it's very difficult to get many plastics clean enough. The same crud that allows the cyanoacrylate to bond prevents the epoxy from "getting a grip" on the surface. And although you can smear it around by sanding first, you can't really get it off reliably. Additionally, you're trying to glue two "flexible" materials with a "rigid" adhesive, with most commonly available epoxies.

PVC cement isn't really a "cement." It's intended to dissolve the surfaces of the plastic so that when the solvent evaporates they're cast into a single piece. Unfortunately, that solvent doesn't significantly dissolve, or even soften, most plastics other than the PVC for which it's intended.

If want to extend your efforts to "glue" picks together, a silicone or "mastic" type adhesive is much more likely to succeed with the materials involved. These are usually "gap-filling" adhesives, and the main difficulty is likely to be with getting a thin enough "glue line." A thin glue layer, uniform and continuous, is much stronger than a thick one, so you need to clamp things tightly together about twice as long as you think it will take for them to "dry," before you try to "wiggle" them to see if they're done setting up.

Almost any decent "silicone glue" may work, if you can get a clean, well fitted joint. Not a particular recommendation, but "EC6000" is a "brand name" general purpose semi-flixible adhesive of a type that might give you a better joint, and is commonly available in craft shops. If you're closer to an auto parts or boat outlet, there are a couple of "body putty" and/or gasket materials - mostly intended for filling dings in auto bodies and/or fiberglass hulls that can sometimes be used as a "glue" for your kind of parts, although they tend to be rather rigid when they've cured.

Making good adhesive joints is as much "black art" as science, although the newer materials are a little more forgiving than the chicken blood that still holds a few wood parts together on early 40s era airplanes.

John