Hmm...there are a number of reasons. First, is the impeller working. There should be a light spray of water and exhaust coming out of some holes halfway up the back of the midsection. If it's not there, then the impeller is bad and the engine is getting hot. That that lead to ignition problems on that motor, even though the engine itself is air-cooled.
Another common problem is forgetting to open the air vent on the fuel tank. The engine will run for some time, but then the tank will develop a partial vaccuum that the crummy little fuel pump bladder in that carburetor can't overcome. Thus, the engine dies and won't restart. That's a good possibility here.
On your fuel tank, there will be a vent of some kind. Loosen it before starting your outboard.
If it runs for 30 minutes, then it's probably not a basic fault in the ignition system, unless it's running hot, as I mentioned.