AFAIR (I had a grill pan that I had to cover with a bit of oil) it would be 1-2 weeks (based on my memory of doing "grilling")

Thin layer of oil out in the open goes bad quicker than oil closed in a bottle.

That's about right, as it's only for searing steak for me. Other pans simply work better for everything else, either stainless or non-stick.

I got the enameled cast iron pan, so it actually works out nicely.