Threadomancy!
Not just the tip but also the can....
So in spite of the tip I had given, I was still having problems, sometimes even with new cans. Storing them inverted (nozzle end down) helps a lot, especially with some brands. I was messing around with an old, barely-used tin which would not spray, when I thought of something a bit last ditch - I shook the can very well, removed the nozzle, and sprayed some WD-40 down the tube from the spray can - OVER SOME SCRAP MAGAZINES as it can be VERY messy. I left the think upright for a minute or so, placed the nozzle back, and left it inverted for some time - about half an hour. I shook it well again, and after some false starts, it worked. I managed to spray a large area before it conked out again, and I had to repeat the process - it worked again.
A word of caution - too much WD-40 and the can will spray large droplets of paint.
In the process I also discovered WD-40 is a good paint remover. Fortunately, this did not affect the quality of the paint on the surface being sprayed.