I have essentially the same policy. Although two minor differences:

1. I will give a student an extension if they ask in advance the first time they ask. The second time (unless it's due to the same situation as the first time... I get a little more flexible with that), the answer is yes if they schedule an appointment with the counseling or learning center to make a plan to ensure that they are making actual changes instead of sticking a bandaid on it.
2. I do not give extensions after the fact regardless of the reason. I have a 10% per day late policy and that's what they are agreeing to if they turn in late work. If they can show me documentation that shows that they were physically incapable of reaching out in advance (for instance, hospitalization). Otherwise, it's a no. I have been criticized for this but I stand by my policy. They can't simply not show up for work for a week without telling their boss why if they want to keep their job. They need to learn to communicate and if they can't do this, they are dealing with something far bigger than what an extension can solve and suggesting otherwise by making exception after exception for them isn't doing them any favors.