Yep I found out recently on here that Southern's DaySave nowadays does NOT require the 7 days but it's easy to get confused as Southern still have the old dedicated, separate DaySave/Networker site running alongside their regular site/booking engine that now offers the DaySave £14 fare through their regular booking engine system.
The period of time in advance to buy a DaySave now appears to be ONLY about havint time to GET the actual tickets that you've ordered online in your hand to travel with, as you must either (a) collect from a SOUTHERN ticket machine [ie at some stations served by Southern services, and NOT others TOD machines at all!] or (b) get the DaySave ticket posted to you = unknown period of time, often next postal day but sometimes later and their site says upto 5.
Starting at EAST CROYDON will allow you to prebuy a DaySave to pick up at a Southern ticket machine there per their site
http://www.southernrailway.com/tickets-and-fares/ticket-types/daysave/
and follow the big button link at BOTTOM of that page, ie to
http://tickets.southernrailway.com/sn/en/landing/promotion.aspx?id=DaySave_Tickets&isAllowed=False
and it even allows SAME DAY it seems!
[Still a bug that their system wont let me put Milton Keynes Central as starting station, even though has a part-time Southern service!]
Otherwise for those who aren't near a Southern ticket machine and who can't wait for a DaySave ticket to reach you by post then as long as you leave one clear working day you can print your own more expensive All Network Downlander for £2.50 more - ie £16.50 - however THAT lacks the benefit of group travel that DaySave has (ie 2-4 people travel for cost of 2 on DaySave).