Here's a recent inquiry from a Best Food Facts reader as well as a response from Dr. Tong (Toni) Wang, Professor in the department of Food Science and Human Nutrition at Iowa State University.
How long will tahini last after opened and should it be stored in the refrigerator?
If the tahini is made like it is in oriental countries – using roasted seeds – it can be quite stable. It can last one to two years under refrigeration, based on my personal experience. Although sesame seed oil is made up of about 40% highly oxidizable linoleic acid (an unsaturated fatty acid - also known as omega-6 acid), the paste is actually amazingly stable. I expect it to be quite stable even if stored (after opening) at room temperature. Personally, though, I always refrigerate it.