J.C. Penney (NYSE: JCP) is at an uncertain time in its history, with many resigned to the fact that the retailer is simply a leftover remnant of a bygone era. The return of retired CEO Myron (Mike) Ullman as interim chief brought new hope to the company, undoing the damage done by Ron Johnson's attempt to give the company a younger image. For awhile, it looked hopeful, thanks to the return of the discounts customers love.

But in its first earnings report since the switch, the company showed no signs of recovery. J.C. Penney's first quarter brought a $348 million loss, up from a $163 million loss in 2012's first quarter. Revenue was down 16.4%, while comparable-store sales were down 16.6%.

Now activist investor Bill Ackman is calling for J.C. Penney's CEO to resign along with board chairman Thomas Engibous. Part of the problem, in Ackman's opinion, is Ullman's behavior, which Ackman believes is more like a permanent CEO than an interim CEO.

But the biggest problem for J.C. Penney is its failure to improve. The company blamed its disappointing first quarter on ongoing improvements to its home departments throughout its chain, but the retailer faces steep competition. That brings the question -- can a CEO replacement single-handedly repair J.C. Penney's problems?

Sears fails to improve

Sears Holdings (NASDAQ: SHLD) is also coping with losses under a new CEO. In its most-recent quarter, the company reported a 3.6% drop in sales for stores open more than a year. The company lost $279 million in the quarter, with revenue falling 9% from the previous year.

When Eddie Lampert took over as CEO in January, it was understood that the CEO faced a challenge. As parent of fledgling department store chain K-Mart, Sears was in bankruptcy when Lampert bought it. To look at the bigger picture, Sears' revenue dropped from $53 billion in 2006 to only $39.9 billion in 2012.

To turn this around, Lampert is counting on technology, with the company's online visitors totaling 18 million in July. But 97% of the company's sales come from its bricks-and-mortar locations, leading to doubt as to whether or not the company's online sales can really make a difference.

Groupon succeeds

On the other hand, Groupon (NASDAQ: GRPN) has emerged from the rubble, reporting a 7% increase in revenue for its first quarter. At one point last year, the company's stock dropped 90%, leading many to wonder if the 50%-off model was a lost cause. But then shares surged higher when news broke that the company was placing interim CEO Eric Lefkofsky in the position on a permanent basis.

In the wake of its earnings announcement that revealed $608.7 million in revenue, the company stated it would have a $300 million share repurchase program over the next two years. The company's growth is especially strong in North America, where revenue grew 45%.

Both Lefkofsky and new chairman of the board Ted Leonsis have been with Groupon since before its chairman was removed in February of this year. Under their leadership, the company has achieved growth in mobile use, with almost half of its transactions through mobile in June.

Who wins?

Relative newcomer Groupon can serve as an example for J.C. Penney and Sears, old-timers who are struggling to compete in an increasingly technology-driven marketplace. J.C. Penney in particular is running out of "second chances" with investors, meaning the company needs to find a solution that works ... and it needs to find that solution soon.

Unlike J.C. Penney, Groupon has adapted to the consumer trend toward mobile devices in a way that works. J.C. Penney could learn something by simply looking around, learning how to reach today's technology-driven customer base, and utilize what it learns to lure in customers. In fact, the company that once used innovation to reach out to customers through catalogs could, perhaps, benefit from using that same catalog approach to win over customers electronically. A new app called Pounce allows consumers to scan items in catalogs and purchase those items with one click. For a former catalog-based company, technology like this could be a great way to win over mobile shoppers. For Sears, mobile adoption could use in-store mobile devices to speed up checking and track down items that aren't in stock. Mobile is here to stay, and the companies that embrace it are likely to be the ones that thrive.

The Motley Fool's chief investment officer has selected his No. 1 stock for this year. Find out which stock it is in the special free report: "The Motley Fool's Top Stock for 2013." Just click here to access the report and find out the name of this under-the-radar company.

Stephanie Faris has no position in any stocks mentioned. The Motley Fool has no position in any of the stocks mentioned. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. Is this post wrong? Click here. Think you can do better? Join us and write your own!