I haven't done Auto-Relist (yet), but I have been studing the options. It's a new feature, so we're all trying to figure it out.
My observations.....
If you uncheck the "Relist with no changes.", you'll see a "Relist with a new quantity of [ ]" and the hidden "When Any items have sold" qualifier for that box (when checked). That might be the solution to the relist, when the count has dropped due to sale(s) and you always want 3 for quantity for new listing.
Also, if it's an always relist situation and you aren't using Inventory to track and aren't worried about supply in stock (said you got 1000), the "[ ] Dont Auto-Relist based on items sold" should always produce a relist whenever the Profiled listing ends. "Any items sold" might mean only when there is at least one sold (and might not include none sold). I noted that issue and am still not 100% certain, but the alternative would seem to avoid the question.
To get the "ball rolling" you do need to add/apply the profile to a saved listing. But, you also need to do a first listing of that saved listing. To cancel Auto-Relist, you locate the active lising on the Active Listing page and use the STOP Auto-Relist button.
Hope those suggestions are helpful and please report back and let the Forum know if it works.
Danno