Stubborn starting question...

I think Waggin is right on! Did you check the gap on the points? I'd clean them with a points file, then set the gap... drive it home, and then swap out the points system for electronic ignition!

I had an Anglia when I was younger that would do that. It would run fine... then start idling a bit rough (sometimes).. I'd shut it off, go into work or whatever, and then come out and it would not start... I's open the gap a bit on the points and it would fire right up. Points can get burned, corroded, or the follower block wears to the point that the points won't open all the way.