Seems simple enough:
"The board decided the complex schedules used at the district’s three high schools didn’t allow for a consistent time for students to recite the Pledge of Allegiance."
When I was in high school, we quit saying it every morning when they integrated the 9th grade into the main high school building, which resulted in literally three shifts of students arriving and departing for classes each day. My junior year I had a 0630 calculus class (don't get me started). The second shift of buses arrived for the first 0745 classes, and the third shift arrived in time for the 0900 class. Our day ended with the same staggered shifts. Classes during the day started and ended at different times. There was no Home Room, no specific time when everyone was sitting down and still where something like the Pledge could be recited. We continued to recite the Pledge before most school functions, except the ones where the National Anthem was played.
It just ain't that big a deal. One high school in Sioux Falls is still saying it every morning, and all of the middle school students still say it.