This must be something that they are changing without telling us. I do not ever remember my loyalty dropping when I move up to the next level. But I just looked in the FAQ, and it says that loyalty drops whenever you move to a different school.
However, this is in the Player's Guide:
Job Changes
During the 3 days of the job period (after the renewal deadline and prior to when new coaches can get teams), you can try to move up to a new division or laterally within a division to a new team. You will lose all of your accumulated recruiting money with any change. To change jobs, you must apply for a job. To do that, you go to the office tab and click on jobs. You will get a listing of all of the jobs available in every division. You may only go up one division (i.e. D-III to D-II) at a time. Pick the school that you want a job at and click on the apply button. Your loyalty will take a hit moving laterally to a new team within the same division that you are already in (i.e. D-III to D-III). The jobs list will list the qualifications of each job and during this time indicate which jobs you may be qualified to take.