Does the engine die? It could be a kinked pressure line.

Sounds to me like it may be wearing out. Once the sleeve and piston wear enough what you are describing may be happening. As the engine gets up to operating temperature the fit between the piston and the sleeve can open up a little too much and you lose too much compression. There is not much that can be done but replace the piston and sleeve. I inhertited an LA 40 with a similar problem. The engine looked like it had fought in Iraq and returned. A new piston and sleeve made the engine run like new.

I'm not saying that this is the problem, but it sounds like a good possibility. The engine is pretty new but may have ingested some dust or had some lean operation. I would check fo air leaks in the engine (backplate, head, carb area), bubbles or debris in the fuel lines, and inspect the tank and plumbing. I would try to rule everthing out before piston/sleeve replacement. You may want to put the engine on a test stand and give it a try.

Pull the muffler off and look at the piston. If you see scratches or if the piston is very dark, you may have found your problem.