Then that cannot be an issue with the charging port on the iPhone, as it is NOT bi-directional. The cable is the bi-directional component of the lightening port standard. The iPhone's female port only has pins on one side, so if the cable works at all (in either configuration) then the iPhone port itself must be functioning fine, else it would not work regardless of which way the plug was inserted.
The issue then has to be with the cable. Are you using genuine Apple cables? The smart chip/circuit in the actual cable is what detects which pins to send power and signal to and enables the ability to flip the cable. If the chip is bad, or it's not a cable from a company authorized by Apple to make and sell lightening cables, then it may not work.