According to the specs for the controller, it "should" be able to output around 10W. If you try to ask more than that from it, it will go into shutdown which results in an output of battery voltage less about a half volt due to rectifier losses. Boosters do that. Unlike a linear regulator or buck converter, they go home to battery voltage when things go all to hell.
Your booster could be hitting the switching limit on current prematurely or just destabilizing. Switching converters destabilize when there's an issue either with a component or in the design. Most simply, that means they fail to control output voltage properly. Hard to say why you're seeing poor output performance off-hand, but it could be due to some issue with the design or possibly a faulty component.