My 89 FLHTC had that same problem,,,found out that Harley had an issue with its starter solenoid,,,incorporated a Ford style starter relay, connecting to battery and starter and also the starter button wire,,,,NEVER clicked after that in the last 10 yrs. I would suggest that when your problem occurs try a jumper wire from battery to starter,,,if it starts that way then a diiferent starter relay is most likely your cure. Good luck
