The difficulty with your engine could be any of several things....

You could have the idle mixture just adjusted to lean. This is rather common, and the engine would be quitting from a lack of fuel.

There could be something bad in the ignition unit. As the engine slows down, the electrical pulse to the spark plug isn't as strong. If there's an internal short or other defect, the weaker pulse might be grounding out, but the pulse at higher RPM isn't. It could be heat-related, since you can start the engine, but it quits after it's been flying.

There's some kind of trash in the carburetor that blocks the low-speed jet.

There could be a bad gasket that leaks after a while...when the engine's had a chance to warm up and get some fuel through it.

To solve your difficulty, the engine should come into the shop.