From your description, it looks like you are not getting enough fuel to the engine to keep it going.
I suggest that you probably have a bad pump or metering needle diaphram. Get a carbeurator repair kit for the carb from your local small engine or lawnmower repair shop and replace both the diaphrams and gaskets. Also check the screen on the fuel inlet to the carb. It may be plugged. While you are at it, spray some carbeurator cleaner in all of the carb passages.