Attach a DMM set to VDC and monitor the 5 VDC. First let us know the Voltage you are measuring and second, see if this voltage drops at all when you get the reset. It also would not hurt at all to replace the 5VDC filter cap. I would do this right now.
Quoted from djriel:When the game is first turned on, the right launcher (that kicks the ball out to the flipper), will trigger about 8-10 times. When the game does the reset, it will also cause that launcher to kick over and over about 8-10 times. It will do this randomly as well, so it's not just specific to the reset.
I would disconnect one wire going to this coil and see if this makes a difference in your random resets. But again change the 5VDC cap, it can't hurt and can only help. Good Luck