I have not had to dig into my Sky Rider to date (unlike my Gottlieb games which I've done a lot of troubleshooting with and have gotten pretty familiar with). I spent some time today trying to understand the problem.
Symptoms:
One player mode, the game cycles through all four players (as if it were 4 player mode) except it's Game Over after ball 5 of Player 1
Game works fine if I start up in 2, 3, or 4 player modes (via the credit button) - goes all the way through Ball 5 on the final player.
Otherwise normal operation - the Players light is correct (1 / 2 / 3 / 4), Player Up light is correct, the score moves through the four players. Need to familiarize myself with the internals and the schematic (a bit different looking than the Gottlieb games) but I should be able to figure it out. I'm guessing it's a wiper / alignment issue with one of the Player Units - so that when it's on One Player it does not close the switch properly.
In other news, I did notice a Player 3 sticky reel (I rarely play more than two players) so that will need some attention, eventually.