Two cycle engines never die. They just wear out. Rings and pistons and gaskets will get old and need to be replaced from time to time, but the engines themselves are very reliable.
Between rebuilds, you're probably looking at 10000km (6000 miles) or so. I'll qualify that and say that I'm guessing here.
I believe that synthetic oil is marginally better, but not even close to being enough to justify the cost --it's a waste of money. Moped engines really don't need that kind of protection/lubrication/thermal stability. However, this is a topic that often starts big wars. You'll get half the people out there saying you're a fool for not using it, and the other half will say you're a fool for paying for it. Same goes with the high/low octane gasoline argument. But it's fun to watch.
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Chris.