If I understand well, the sell offer remains live forever unless the seller puts its down himself, right?
The offer is technically always there, however when the quantity goes to 0 it will no longer be visible publicly (so if you sell out, you can just change the quantity when your stock replenishes). To hide an offer you can either change the quantity to 0 or change it to a private offer.
Is there a way to browse your market from a browser (without downloading SYS client) ?