I don't know how badges work and if/how one can be created but I am surprised there is no badge for asking a question every day for 'X' number of days. Is there any reason why not? If not, is there any interest in creating one?
I would oppose such a badge.
It would be wonderful if everyone used this site to ask about the interesting problems you encounter in your day-to-day activities. But when you're suddenly put on the spot to "ask questions daily," you'll likely end up with an influx of low-quality, uninspired questions. Inspiration and intrigue doesn't run on a schedule.
Users should be asking real questions about problems they actually have. Don't add a badge or other incentive to force the issue. You won't likely get the results you are trying to encourage.
I like this idea, or at least a variation thereof to encourage asking good questions. I think it would have to exclude negatively voted or duplicate questions, and possibly even questions with a score of less than some number (5?). I'm thinking along the lines of 10 straight days for a bronze badge; no silvers or golds.
Proposed name: Inquisitive.
Although it seems this idea has been proposed and rejected on meta.SO Badge for asking questions
Something similar has recently been approved over on MSE. I will hereby being taking credit for the badge name.