I think the answer lies in recharging the battery fixes the problem until the next time. It sounds like your battery is going dead.
Goldwings are funny animals. When the battery is weak, there will be enough juice to turn the engine over just fine, but the draw from turning the engine over doesn't leave enough for the electronic ignition to create a spark. Usually when this happens the engine will turn over but not fire until you release the starter switch. At that time, the available current goes back up and the engine coasts just long enough from the starter turning it over so that it fires and starts up. When it's cold, it is harder to start, so you end up charging the battery. When the battery is charged up you have enough current for a short while to power the starter and the ignition system.
Next time try jumping the battery and see if it starts right up. If it does, that verifies that its a bad battery.
If you will invest in a battery maintainer, your next battery will last much longer. Notice I said battery maintainer, not battery charger.