Despite the pandemic and the needs of her aging mother, she still goes to the store because she doesn’t trust Amazon, Instacart or Walmart to get it right. “If someone brought me something that wasn’t ripe I would not be happy,” Yore says.

She’s not alone. Among those who use online grocery pickup services, only half include produce in their orders primarily due to concerns over quality, according to Field Agent, an industry researcher. Fresh food is the thing that consumers are most likely to buy in physical stores exclusively once the pandemic subsides, according to research from Evercore ISI. Items like bottled water, pet food and other bulky, non-perishable household staples have better prospects online, due to the hassle of lugging them out of stores.

Groceries are a critical battleground in the retail wars. Walmart started out selling only general merchandise but embraced groceries to lure shoppers into its stores regularly. Amazon has pushed into grocery over the past decade as a way to reach the delivery frequency needed to offset the billions it spends on shipping.

The pandemic poured rocket fuel on grocery delivery as stores curtailed hours and customer counts, and who cares when the truck shows up if we’re home all day? Even the founder of notorious dot-com flame-out Webvan is now back for another stab at the business.

Limited demand and the high cost of last-mile delivery serve as the main obstacles for successful online grocery ventures. It works in densely populated cities like New York because couriers there can make multiple deliveries per hour. The suburbs are much trickier, and volume is key to bringing the costs down.

Walmart, the nation’s biggest grocer, has largely avoided the unfavorable economics of home delivery by focusing on curbside pickup, now available at more than 3,600 of its 4,750 U.S. stores. The free service appeals to suburban and rural consumers because they can schedule it when convenient, rather than being beholden to a random delivery window.

Despite Amazon’s dominance in e-commerce, fresh food is the one area where Walmart maintains a clear edge over its rival. More than half of purchases made on Walmart’s website were groceries in the first quarter, according to researcher M Science, up from 38% at the end of last year. Indeed, Walmart has been so successful with groceries that profit margins have suffered, so the company recently merged its food-shopping app with the main app so customers can put a few higher-margin non-food items in their carts next to the bananas and bread.

As retailers jostle, the next few months will be critical in assessing the lasting effects of the pandemic on shopping habits. Recent data is muddied by the stockpiling of late March and early April, as well as government stimulus checks that buttressed consumer spending as millions of jobs evaporated. Signs of strain are emerging: Shoppers used credit cards to pay for 46% of grocery transactions in April, up from 27% in December, suggesting people have less money to pay for basic needs, says Ted Rossman, an analyst at Bankrate.com.

The key question is the same as when Webvan went bust 20 years ago: Will there be sufficient demand to justify the costs?

“What drove the rapid increase in online grocery’s penetration? It was fear—fear of catching the virus,” says David Bishop, a partner at retail sales and marketing firm Brick Meets Click. “Anyone who is rooting for online to stay at this rate, unfortunately, is rooting for the virus.”