As a practical matter, no one has bumped up against these limits yet, because there are plenty of UAV operators for the Shadow 200 and Raven UAVs that comprise most of the U.S. Army fleet. And if there were an emergency situation requiring an operator to stay at the controls longer than the regulations allow, it would happen.
U.S. Army UAV operators have restrictions on how many hours a month they can spend operating aircraft. Monthly, they can spend 140 hours at the controls. That averages out to less than five hours a day. But in any single day, they can spend eight hours at the controls, and that goes down as the time period gets longer (in any three day period, only 22 hours at the controls.) There is also an adjustment made for troops working at night. One hour of "night flying" is equal to 1.4 hours of day flying. This takes into account the fact the people are not as alert at night. Thus, the max flight time, in 24 hours, if all work is done at night, is 5.7 hours.