I'm not sure how long, but I went to test a theory of if it will save what you sold until you logged out, but when I checked my buyback tab, some of the things I sold yesterday where still there. I have also in the past been able to buy back things even though I switched zones.

I wouldn't use it as extra bank space, but it is quite helpful if your inventory is completely full and there is nothing you want to trash, but you need at least 3-4 spaces in your inventory to refine or deconstruct items, you can sell some things to make room and buy them back after.

In my experience once I log out the stuff I've sold is gone when I come back.