You may want to read the Background on how PWR matters for tournament selection and How the “can make it at-large teams” can make it sections of NCAA tournament possibilities (with less math), if you haven’t already.
How Notre Dame could miss
Given that Notre Dame is already #12, there are myriad ways to get the Irish to 12-13, totaling about 60% of total remaining scenarios (see Notre Dame PWR details).
Because that 12-13 range is the lowest the idle Irish can fall, the most important contributor to excluding Notre Dame is to have conference tournaments won by low-ranked teams. That chews up spots that could otherwise have gone to at-large teams, what we call “moving the cutline”.
For example, the following scenario has Minnesota-Duluth flip its comparison with Notre Dame to push the Irish down to 13. It then has 4 other conferences won by teams that wouldn’t have otherwise auto-qualified:
Those factors come together in about 7% of remaining scenarios.