I keep mine in the fridge, & I've never had a jar go rancid on me or have any change in taste or texture (& we're talking 6-7+ months here).
I don't bother turning the jar upside down, because the product still ends up separated (just like natural peanut butter), & you have to stir it all together anyway. I just take a long ice-tea spoon, skewer, or cooking chopstick & stir away (just like I'd do with natural peanut butter) until everything is homogenized again before I use it.
Kept unrefrigerated, sesame oil & sesame-oil products will tend to turn rancid before peanut-oil products. I don't know why, but they do. I've had bottles of peanut oil last far far longer than bottles of sesame oil. Maybe because peanut oil for cooking is processed more than sesame oil?