I've been told that shortbread cookies will last a year, or more, if kept tightly covered in an air tight container. However, I can't imagine trying to keep cookies "fresh" for that length of time. I would guess that, in the air tight container, they might still be pretty good after about thirty or sixty days (you might even want to stretch that to three months) but I wouldn't try it for any longer period of time.
If you're willing to experiment (like putting them in separate containers and seeing how they fare at thirty day intervals) let us know what you learn from your experience please.
My failures in life are few. The most blatant of these is my attempts at retirement. I've studied the process carefully but cannot begin to understand how it is done.