zephyr,
what is the time between spindle start ups?
Does the spindle start fail on a restart after a shorter down period only?
In that case one of the electromechanical elements might not get enough voltage and/or current. Typical indicator is that there are no problems after a longer period of time, because the circuits have a longer time to build up the "juice". Could also be the difference between "clink" and "clock" or what ever you heard
.
If this is the case then there might be some capacitors/induction elements on your motor/spindle control board history/bad/old.
A cold connection on one of the wires sounds unlikely to me but you always have the option to strenghten it with some solder into the existing connection