I had a Honda Handi 3KW unit years ago. After about 7~10 days in Mammoth CG (elevation ~ 6200 MSL) Yellowstone, it would not start. Turned out that the spark plug had fouled. Once the fouling was cleaned off, it when back to its' easy start, rock-solid reliability again. Shortly after the cleaning, I returned to a lower altitude and never had a problem.
Honda has a "High Altitude Kit" BUT, recommends that it be installed by an authorized dealer. It would then have to be changed back once I returned to sea level. Too costly and troublesome as far as I was concerned. In years past, some carbs had user adjustable carbs. I was told by a small engine repair shop that the laws had been changed preventing manufacturers from offering that owner adjustable feature. If that's correct (and I believe it is), it's just another example of the government knowing what's best when the truth is that they often don't have a clue.