2 things come to mind for me here. The first is a plugged up internal fuel filter (inside the carb). Those plug frequently and are very easily cleaned. Second is not so common, but sounds possible from your description. That's low ignition voltage. When the battery pack draws down to a certain point, it puts the engine into a "limp" mode, cutting power drastically. As mentioned, you don't see it often, but when you do it sounds for all the world just like a carb problem - similar to what you are describing. When measuring that battery voltage to check, make absolutely sure you do that with a draw on it - as in after the systems been turned on for a few minutes.