When you change the grading period of a course section, all assignments will default as "No Grading Period." I then have to manually enter the course to change each individual assignment's grading period. Schoology should change the default from "No Grading Period" to the chosen grading period of the section.
I spoke with Schoology Support and was told that this is the intended behavior and that it was a limitation. If I choose 1 grading period, when would there be a time that I would not want an assignment associated with that 1 grading period? Instead, the default of "No Grading Period" should apply only when there are multiple grading periods added to a course section.