<li>Are these spark plugs you are using <i>brand new</i>? Are you using the right kind?</li>
<li>You said that cleaning your carburetor fixed the problem the first time and then after 3 hours it stopped working again. Have you cleaned the carburetor again? If your tank is dirty/rusty, it can clog your carburetor up very quickly.</li>
<li>Is it possible your petcock is bad? I've seen them go intermittent where fuel will flow fine for a few hours, then barely come through, and then flow correctly again... The next time your moped dies on you, disconnect the fuel line from the carburetor and verify you are getting a decent fuel flow.
<li>If you've ever removed your flywheel you'll know what the key is: it's a little notch on the crankshaft that fits into a little groove on the flywheel that prevents the flywheel from getting "out of sync" with the engine.</li>