The headphone presents a reactive, not resistive load to the amplifier... looking at the phase angles will tell you that the load at resonance is mostly inductive (if it wasn't you could imagine how terrible it would sound with the driver being completely undamped at resonance). Most solid state amps in my experience don't have a problem driving an inductive load, even ones with a relatively weak power supply. Your problem is more likely higher in frequency ~200hz, where the load is far more capacitive and the current demand may outstrip what a portable amp is capable of providing.