I realize that there are rules in place that prevent posters from deleting their own questions, but I would like to see a disincentive for deletion. One possibility is to flag a "delete rate," similar to the existing "accept rate": if you see that a user has deleted many of his/her questions, you'll know that any effort you expend in an answer is likely to be wasted.
(and yes, this was driven by recent experience)
Based on the votes, it appears that this isn't a very popular idea. However, I feel that some answers to the responders are warranted.
I'll start with the straw man first: yes, it is conceivable that a user with a 100% deletion rate could come up with a good question and decide not to delete it. And I'm sure that it is equally likely that there will be a responder who sees the 100% delete rate, but decides to take a chance on the question anyway. Particularly if the answer is simple.
Is this a reasonable scenario? I don't think so; truly bad questions are quickly picked up by the Close Police without any input from the OP. However, I think a disincentive actually works here: it drives the user toward positive behavior, such as editing the question and making it better.
OK, on to the user who realizes that the question is an exact duplicate. Again, duplicate questions get closed pretty quickly. However, this concern could be satisfied by giving users the option to close their own questions.
Next: "recoup a deletion rate" similar to recouping a low acceptance rate: personally, I feel having users quickly run through and accept answers in order to improve their acceptance percentage is actually a bad thing. Acceptance should be a statement that "I have tried this answer, and it works for me."
And finally: realizing the answer immediately after posting the question. To which my response is: OK, you had this problem, do you think you're the only person in the world to have it? The proper response in this case is to prepare an answer, so that other people don't have to ask the question.