So once upon a time, I used to work at a Big Publishing House that made textbooks, which have crazy-tight and crazy-serious deadlines. And as I learned most of my publishing process there, deadlines being really fucking serious business got firmly entrenched in how I do things.
I don't miss deadlines.
And blowing a deadline for me is the shortest route possible to never working for me again, full stop, no exceptions, no joke. You've demonstrated that you are not reliable at gauging your own time, your own process, your own life, and you're not taking responsibility for the choices you make and how you communicate with the people you work with. And there are so many other fish in the sea that I don't need to put up with that from you, ever again.
The email saying, "Hey, I won't be able to make my upcoming deadline," that's fine. That does not set the emergency lights spinning and the klaxons wailing. That email is, in fact, awesome.
That email, which is sent as soon as you know a deadline is going to be a problem, keeps me in the loop, lets me make informed decisions, and shows that you're taking responsibility for whatever the problem is, whether it's a schedule oversight or a life-and-death hospital emergency. That email, which also should include a revised deadline, lets me adjust my plans now, while I have lead time, instead of three days after the day I was expecting to get work back from you.
That email is how professionals and equals communicate, and I probably respect you more, not less, when I get it. Because we all know shit happens, the important thing is how you deal with it.