At a previous position, I had a co-worker who was always dealing with some kind of emergency request or crisis that had to be taken care of right away. No matter what time of the day or what else she had planned to do. She never learned one of my cardinal rules: A lack of planning on your part does not constitute an emergency on my part. She was always in a frenzied state and was always at wit's end. I was constantly after her to learn to say No when confronted with yet another emergency request. By doing her job in this manner, she was inviting her user community to ignore proper planning and causing herself more grief than was necessary.
Sean Gallagher has a term for this: IT-codependence.
There's a fine line between being "agile" and being an enabler of a dysfunctional business model. You're agile if you've got a process that incorporates flexibility and plans for "ship early and often" approaches to problem-solving. You're an enabler if you constantly have to go back and fix implementations you rushed to make business deadlines so that they'll scale or to integrate them into your architecture so you can support them...or if you don't have the time to do either of those because of more rapidly emerging business requirements.
It is a tough habit to break, but one that will make every one's life better and will produce better results and stronger solutions. If you find yourself in such a situation, biting the bullet and saying No might be a scary proposition, but anticipation of the pain is always worse than the pain itself. Who knows, you might even gain some respect for standing up for yourself.