Particles appear/disappear when they should live forever.

I've got some particles set to appear at rate 0.5, number variance 0.1, lifespan 1000 (also tried 99999), lifespan variance 0. I.e. intending for them to build up on screen. It is a 60-frame animation.

When I press play it seems to be okay. But when I render, a few of the particles seem to be flashing on and off. (They are not visible at the end - I think they are just appearing for one frame?)

NO: after trying different seeds, I see the same problem in normal playback, too, not just when rendering. But, in playback, it looks like it gets to a certain frame, then regenerates all the particles in different position. In the rendered movie it is the flash on/off effect. ...ah, if I do playback after rendering, then I see the flashing.

I've tried different seeds, switching "time lock" on and off, trying all three values of "Temporal Dist.", and locking the pRender node (also the Merge node that comes immediately before the Save node). All without success.
(Changing random seed is having an effect: sometimes it is only 1 or 2 particles that are flashing, sometimes it is up to a dozen.)

After thrashing around for a while, I got a good render. I had switched off "Automatic pre-roll", and pressed "Pre-roll" a couple of times, then did the render. Does that sound like an explanation, or coincidence?

(BTW, everything in quotes in this message are settings I don't yet understand )

(I'm on Fusion 9.0.1, build 3, Linux.)

I always cache particles to disk (right-click on the node) for rendering.

"a few of the particles seem to be flashing on and off"

My solution to this problem was to go to the style menu in the Inspector and change the minimum on the fade control to very slightly above zero (0.1 worked for me) so that these unwanted particles hadn't had sufficient time to fade in by the time the next frame was reached, at which point they were gone so you never see them.

That fixed it for me.