Ah, I was using the nut to tighten them in. Doh!
Therein lies your mistake. The nut is only there to keep them in place once installed. They should be pressed or hammered in. The nut will never pull them into place as the thread simply isn't strong enough.
Support bottom of the crank before hammering to protect the BB. Tighten the nut first, then drive it in with a few good cracks with a hammer (you don't need a huge hammer, a typical 1lb claw hammer is enough), tighten the nut again and then hammer again and repeat until the nut stops coming loose. Ride about twenty miles and check again.
It can be worthwhile to file the taper a little flatter before installing. Some modern replacements seem to have very oblique angles. A more shallow angle will have better purchase on the spindle and will be less likely to bend or come loose in service. Compare it to the old ones if you have them to see if it's close. The skill is in filing it and keeping it flat and having both of them as close to identical as possible or the cranks won't line up properly. Not something you can rush but worth spending time on.
It's a simple but crude design but if installed properly there will be no problems with them in service.