No, Harley-Davidson motorcycles do not stop running once they start. Like most motorcycles, Harley-Davidson motorcycles are designed to stay running once the engine is started, provided that the necessary conditions are met.
Once you start a Harley-Davidson motorcycle, the engine will continue to run until you turn it off using the ignition switch or by cutting off the fuel supply. The motorcycle will maintain idle or run at the selected RPM unless there is a mechanical issue or you intentionally shut off the engine.
It's important to note that if a Harley-Davidson motorcycle experiences any mechanical problems or malfunctions, it may stop running. However, under normal circumstances, the motorcycle will continue to run as long as the engine is operating correctly and has a supply of fuel.