A better question would be "Is the U.S. flag required to be lowered when a U.S. soldier dies in service to his country?"
Haven't found any info on that; but several sites mention that only the President or state governors can order the flag to half staff.
Judging from the website you linked it looks like the respective state governors order the flag to half staff when a soldier from their state is killed in combat, or on such a day that the governor specifies.
All of our fallen soldiers are honored every year on Memorial Day.
from
http://www.gettysburgflag.com/FlyFlagHalfMast.php: the "
How long should the flag be at half staff?" section
"On Memorial Day, the day set aside to honor all the people who have died while serving the United States & originally called Decoration Day, the flag is flown at half-Staff until noon, then raised to full staff until sundown."
Never knew about the half staff until noon part, I've always flown it all day. Of course I never knew about flying the black ribbon when the flag can't be lowered either.