That's an intriguing observation. At first glance one might suspect that the Motor 1C switch could be intermittent:
Solar City C relay (resized).jpg
but the blue-black wire that leads from it also goes to the 10/100/1000 Point relays and other things (not shown) so unless those are acting up too I don't think that's the problem. Assuming that all of the drop targets become unresponsive I'd look for an intermittent connection to the drop target banks, especially the blue-black, maroon-yellow and white-blue wires that connect to it either where they attach to the drop target assemblies or perhaps at the jones plugs. The idea that a drop target reset can make or break the C relay may point to a loose or bad connection.

When the C relay isn't working, are all four of the rollover switches that could fire it also unresponsive? Only two of the four are ever enabled at a time so try all four to see if any of them work.

Another approach would be to experiment with the game adjustments. In particular if you change to 3 balls per game and 500 points per side drop target does the D relay start to misbehave too?

/Mark

Can you clarify? Do the round targets stop working too? They're not related to the C relay and should just score 100 or 1000 points depending on your configuration. In fact the two rollovers that return the ball to the flippers are also not tied to C but should just score 1000 points. Do any of the 10 point rebound switches work when C doesn't fire? If any of these other things stop working then maybe your issue is with the Motor 1C switch at the bottom right corner of the schematic above after all.