I don't know why it's doing it every other frame but the reason you see it with mental ray is because it's ray tracing it (you achieve the same result without MR by turning on raytracing in the maya software renderer, actually might be worth trying this to see if you still get the problem).
Xander-0: he's talking about particles in relfections not opti fx which are a post process done by maya after the render finishes, hence why they don't appear in reflections
A
Technical Director - Framestore
Currently working on: Your Highness
IMDB