Make admission free to all students that show up to the gate with a valid student ID. This removes the chance for a student to buy season tickets and not show up to certain games...leaving empty seats. It also keeps students from turning it into a profit scheme.
The athletic department could even open up "student guest" tickets on the Monday prior to the Saturday game where students could purchase an extra ticket for a friend or family member. Perhaps cap these at ~100 per game and sell them at the reduced price that the faculty/staff pay. You are guaranteed these tickets will be used because of the price being paid for them.
By selling ticket packages in their current format...the supply has far outweighed the game day demand. Like I said before...cut the student section back down to 12,000...make it free admission with a valid student ID...and sell an extra 100 or so student guest tickets the Monday of the game week. I guarantee you the problem of student attendance would disappear.