By the time Kalliope had infiltrated the academy, the guards and soldiers had more than enough time to launch a counter-offensive to retake the walls and the school. Their numbers far exceeded that of the insurgents, but they had one thing that kept them from making a move and that was hostages.
Not only was the academy the location where most of the city's mages stayed to perform research and teach, but it was also home to a large concentration of the heirs of many of the country's noble families. There was no way to know how many noble children were alive, but if they made a move too rashly, it could result in more deaths.
They were paralyzed into inaction. After Kalliope's infiltration, the enemy had tightened their defenses and spread their barriers to encompass the entirety of the walls around the academy. Infiltration of any kind moving forward would be nearly impossible.