As Amazon and Walmart push their way into consumers' online grocery carts, Peapod—the elder statesman of the industry—is fighting back. But it won't be easy to win long term.

"E-commerce is exceptionally expensive and hard to make money on, especially as customer expectations have risen," says Mikey Vu, a partner with Bain & Company. Free same-day delivery timed to the minute is "incredibly hard to do. For Peapod, it's even harder because they don't have the scale of Amazon."