Depends what you consider shot down. ALike actually pursued them/ask them out and been told NO. Then no, I haven't. But then again, I haven't really asked anyone out to do be told no.
Now I have wanted more out of a relationship and been told the person wasn't interested in more than a casual relationship. Twice in fact. My last two relationships have been more casual than I would have liked.
How did I handle it? No very well. A lot of tears. A lot of music "therapy." A lot of drinking.