Since its intermittent, it is probably a connection issue - a ribbon cable likely, but could also be a lead of a PIA or something on the CPU board.
Could be something like when the game warms up, a connector warms up and completes a circuit, or the opposite, once it warms up, it loses connection.
That analogy could apply to the ribbon cable, either end of it, or anything along the way in the circuit.
The segment that is out in the pictures is segment 'g'
Look at page 63 of your manual, which is in the fold out schematic section, and trace segment g back through the display board to the CPU.
Note that you are looking for segment g - not segment g' - the ' means it's on display 3 and 4
It looks like segment g goes back through U12 to connector J1, which mates to the ribbon cable that runs to 1J22 (the ribbon cable) on the CPU. Specifically, 1J22 Pin #25. It also goes through SRC2 to pin 16 of U41, a 6821 PIA.
So, somewhere along the way, I would guess you have an intermittent connection. I'd start with the ribbon cable. Wiggle each end of it carefully with the game on, and see if the segment goes away and comes back as you wiggle it. If it's not that, then I'd carefully pull the display and check for cold solder joints along the path as listed in the schematic, as well as the CPU.