Is the GetNthRecord an auto-entered calculation for a date field or a calculation field with "Date" as the result type? I would expect a calculation field to update automatically, but there are details that might keep an auto-entered calculation from updating though I can't tell from your post if those "details" are a factor here or not.
It is an auto-entered for a date field.
Why not define it as a calculation field?
I suspect that this field is not defined in the student table. Auto-enter calculation will not automatically update when data in a field from a different record or table is modified.
Another option is to set up a script trigger on the TotalDaysAssigned field to perform a script that uses set field to update this date field.