Should I delete a question with many down-votes? The question is informative, but people are continuously down-voting it, causing me to lose my reputation.
You cannot delete your own question when there is an answer that has been up-voted (at least twice, if I correctly recall).
That said, on Meta Stack Overflow the down-votes have a different meaning. In most of the cases, the down-votes on meta sites mean disagreement with what implied from the question, in your case, that it is a good idea to report a link to a question asked elsewhere instead of rewriting the question on the Stack Exchange site where you wanted to ask it.
Generally speaking, it is preferable to avoid deleting your own questions because, if you delete too much of your questions, you could not be anymore able to ask new questions until you don't gain reputation by answering questions.
I understand your reputation loss but even -10 votes means "only" -20 reputation which can be amended by meager 2 upvotes on answer you make or 4 upvotes on other question - really not that hard to achieve.