Sometimes it is simply that a faint coating of rust has developed onto the flywheel magnets that induce the ignition coil to spark the spark plugs as the flywheel spins. The rust can show up from simple condensation as temperatures get cooler or that we let water from rain or water from hosing get in there. Check and see if you have spark at the plug and if you don’t that is a good sign it is in the magneto assembly which comprises your flywheel and the coil that could be bad if you find no rust on either of them.
[edit] I think I misunderstood your description of what’s happening, it sounds like your starter bendix gear and/or spring is worn or broken. Sometimes the windings in the starter itself will get a dead spot that will require it’s replacing if the bendix gear and spring check out OK.
[edit] I think I misunderstood your description of what’s happening, it sounds like your starter bendix gear and/or spring is worn or broken. Sometimes the windings in the starter itself will get a dead spot that will require it’s replacing if the bendix gear and spring check out OK.