check the capacitor - it may have broken off or is missing. You need it for the quick hits otherwise the hit will not register. 0.047Microfarad

As mentioned above, the switch caps are a great place to check. Make sure they are all there for the switches specified in the manual and make sure that your swap out the original ones as they will fail (if they haven't already) and can cause some weird issues like phantom switches activating. You can replace them with 0.05uf caps as the 0.047 are harder to find. I get the ones from either Ed at GPE or from Tayda Electonics. The second thing I would check would be the connectors and headers. Those old connectors likely need to be re-pinned if they are original. I get my pins\headers from Ed at GPE as well.
My Space Invaders is in 1000 pieces right now being restored, but I had to re-pin every connector due to corrosion and and burnt connectors. I replaced all the headers as well.