[Rules] Hex Control (once again)

[campsawyer]

I had an interesting issue come one in a Skype game with Hugmenot tonight. It opens up the hex control discussion again. Here is the situation,

A German unit controls a hex. An American unit assaults the German hex and demoralizes the German unit. In a later activation, the American unit is demoralized too. The American demoralization happens after the initial American assault and no other American or German units enter the hex after that. If fact, by the end of the turn everything stays as is and both units remain demoralized. Which side controls the hex at the end of the turn? Or is it uncontrolled.