This season's consumer behavior is demonstrating that, to an extent, consumers are willing to shop online at both formats (Sears and Kmart). However, consumers are demonstrating that they still prefer not to shop in the stores, which is a problem. Many other retailers see satisfactory performance in-store and online, while it is sounding like Sears and Kmart's only saving grace is online, which does not bode well for the stores and may not bode well for the company overall as both sources of sales need to be strong.
Just because web orders are "up" does not mean that Sears and Kmart are "out of the woods", so to speak. It is not a solid reason to keep the stores around as the stores still need to demonstrate an appreciable amount of foot traffic, in-store sales and most importantly, profitability. There is no reason to staff a retail store if the only thing that is keeping it open are online order fulfillments. Otherwise, it just makes more sense to get rid of the stores and convert to an online-only presence, and that is if Sears Holdings does not liquidate.
One other thing to be aware of: Sears and Kmart may be experiencing an uptick in online orders principally for the rewards promotion (i.e., get $250 back in points if you spend $250, $600 back in points if you spend $600+, etc.). If Sears Holdings does not uphold their end of the bargain by issuing the rewards points as advertised, it will cause irrevocable harm in the sense that they will alienate and virtually lose their entire customer base for good. Their public perception would be permanently damned, and that is something Sears literally cannot afford to risk.