I've been using the same bottle of toasted sesame oil for at least two years now with no ill effects
I keep mine refrigerated.
oil rancidity doesn't cause ill effects in general, just off smells and taste. Which, if you don't notice, is fine, the more things taste good to one, the better off one is.
What kind of sesame oil are you getting...
I think unopened sesame oil can have years of shelf-life. I certainly never had a problem with the smell and we use sesame oil quite a bit in our household.
Same for me - I’m quite sensitive to rancid oil and have never experienced an issue with any brand of sesame oil kept unrefrigerated for a long period of time.
Refrigerate it and the shelf life after opening increases greatly.