The level in the tank doesn't matter. Like how much gas in in your car's tank doesn't effect how it runs.
The quality of it is what's important.
Just a wild guess, but if that gas is old, it'll go bad, or the 'goodies' evaporate out over time.
I've only had lanterns, but they pretty much work the same as a stove.
I've had better luck running them totally empty to store them very long.