This is already in place - the system itself is auto bumping questions with no accepted or upvoted answers after certain amount of time.
It's done through the Community user account. I couldn't find the official statement about this mechanism but it's explained pretty well in this question here on Meta with Jeff answer giving some technical details as well:
Just to be 100% clear, our definition of unanswered is "no upvoted answers".
I recently tweaked the community bumping so that it favors unanswered questions with lots of views. Right now it takes the top 100 unanswered questions with no recent activity by views, then picks randomly from within that group.
I think it's done after two months of inactivity (no new answer or edit) and when question got answer with upvote it won't get auto bumped.