It is very likely a tunning issue. Unfortunately we can't tell which way you need to go with what you've said. If it's to lean (not enough fuel), the engine will start to get too hot and do what you describe and if it's to rich (too much fuel) it will do what you describe.

At a safe altidude and location that you can perform a dead stick landing from when the engine is lagging, smoothly yet somewhat quickly advance the throttle to full. Observe your exhaust. If you get a more than normal amount of smoke and probably a sputter... it's to rich (turn your needle in, clockwise, two clicks and retest). If it dies without any smoke, it's likely to lean (turn your needle out, counter clockwise 2 clicks and retest).

Aditionally, what does your plane look like after you land. Is it absolutely covered in oil? Is it as dry as a bone in the desert? Do you have a constant yet faint smoke trail behind your plane when flying at higher to full throttle settings? At mid throttle, it is hard to see the smoke.