Starts to sound like a wiring issue---either the wiring itself or a switch-operated solenoid. Trace out the wiring--a good schematic will be beneficial--and see what goes where and what the electrical 'control' (switch, fuse, solenoid) look like.
Before going too far test your male phone power plug in a known good power outlet on another vehicle or power supply. Try unscrewing the tip from the male power connector and checking its internal fuse with a meter.
I've found some of the male power plugs fairly delicate (not the plugs themselves, but the internal wiring and tiny circuit board). Try a different 12-vdc phone charging cord with your device.
A caveat concerning any type 12-vdc power outlet / source / receptacle in any mobile application, powering any electronic device, based on my experience in the amateur radio world: run both hot and ground from any power outlet back to the battery and fuse both lines at the battery. May save some expensive electronics.
Please post back your continuing experiences so we may all learn.