It can be weak on its own, if I am not predictable. But if I combine it with more specific precomittments, then other agents who plan to exploit a one time excuse, where part of convincing me not to carry through the threat, is that I can precommit never to allow that excuse again, can predict that I will wish I had precommitted from the beginning to never allow that excuse at all, and therefore act as if I had made that precommittment, and still cary through the punishment, so they should not provoke the punishment planning to offer that excuse.

This greatly strengthens any specific precommittment I make, by preventing the exploitation of one time excuses. If an agent wants to offer me an excuse, they will need to be able to convince me that I should always allow that excuse.

In the grieving student example, I am willing to allow the excuse for the same reasons that I am willing to explicitly ammend the precommittment to allow an exception in those circumstances.