For the life of me, I can't figure out why an emitter stops emitting. There doesn't seem to be a property to control this. I would assume the "particles/sec" can be animated to stop/start emitting when desired, but I haven't changed that property.
I have it fixed at 200, and a few seconds into the timeline... particles cease to emit.
Particles/sec is the way to control emission, yes.
Possibly you are using a custom particle with the "Current Time" sampling mode. If the clip/comp you use as a particle ends, *all* particles go blank. This is different from when emission stops, then the already born particles would still be visible, but no new ones would be emitted.