The first thing I would check is the game over relay. On this machine, the game over relay is a latch-trip unit, with two coils. The latch coil pulls in the relay armature to assert the switches of the relay. When the relay pulls in, there is a latching plate that drops into place via spring pressure to keep the armature in the asserted position. In this way, the relay can be permanently set to the asserted state with just a short pulse to the latch coil. The latching plate itself can be pulled in by the other coil of the relay (the trip coil), which releases the armature and allows it to go back to the non-asserted state via spring pressure.
The game over relay is supposed to latch via a short pulse to the latch coil on game start. If this relay doesn't successfully latch, you'll get the symptoms you are seeing. Often times the latching mechanism itself is dirty and needs to be cleaned and adjusted. Sometimes the spring on the latching plate has gotten too weak to put the latching plate into position on game start. And, sometimes the latching assembly (latching plate and trip coil) is out of adjustment and the entire assembly needs to be moved slightly to get things working again. Another somewhat common issue is that the inside face of the latching plate has gotten gummed up and /or slightly magnetized such that it is sticking to the center pole piece of the trip coil, preventing the game over relay from latching.
If the mechanical operation of the relay seems OK, but the game over relay is not latching on game start, then you'll want to look at the switches in the circuit that pulse the latch coil on game start, because there is probably a switch in that circuit that is dirty and/or out of adjustment.
There are other issues that can cause the symptom you are seeing, but this is probably the most common one, so it's a good place to start troubleshooting.