As particles are dynamics they are calculated on a per frame basis, jumping to frame 120 might be messing up the calcualtion.
Try cashing the particles and then rendering form frame 120, as i'm guessing that mayas attempting to calculate them based off 120 as the start, not knowing whats happened before (even though nothing has) due to it wanting the calcs to start off at frame 1, caching them from frame 1 to 300 stores the data so it just references the positions of the particles from the cache with no calcs and should stop the strange ones appearing from the clacs on the fly.
"No pressure, no diamonds" Thomas Carlyle