No, American citizens are not in the process of "losing" their rights to trial by jury.
Now, some Americans can be DENIED the right to a jury trial if they are caught fighting Americans on a battlefield, as more than 1,000 Americans found out during World War Two after answering Hitler's call for all Aryan's to return to Germany to fight for the Reich (7 of whom were sent back to America to engage in sabotage via U-boats), but you don't stop a battle to hold a trial for your enemy simply because she still has U.S. citizenship (you simply shoot them).