Shopper fatigue over rising prices might seem like a good thing for discount stores as more people hunt for bargains. But falling shares of Dollar Tree and Dollar General stores show the pressure on their core consumers.

The discounters' stocks both fell more than 6% Friday, before paring some of those losses by late afternoon. The declines placed them among the worst performers in the S&P 500 for the day. It's not just a one-day slump either: both stocks are roughly flat for the year.

Investors are "having concerns around the health of the consumer and rising oil costs after trading heavily into the retail sector yesterday, as higher oil prices can lead to higher inflation," Morningstar's Brett Husslein told Barron's. "We think investors were seeking a safe-haven that is reasonably insulated from AI-related themes yesterday and are now giving up those gains they saw the prior trading day."

While high prices can motivate more affluent shoppers to hunt for deals wherever they can find them, the chains' core consumers are being forced to pick and choose. Overall inflation combined with high fuel prices -- oil futures are trading at five-month highs, while gas prices are up more than 40% since the Iran war started -- hits lower-income shoppers harder because they have less discretionary income.

"That is forcing consumers, especially at the lower end of the income distribution, to deploy their purchasing power more consciously," PwC economists wrote in a recent report. "Consumers are still spending, but they are increasingly selective about where they spend and what they get in return," the report added.

While Dollar General's sales come mostly from consumables like shampoo and snacks, 18% come from more discretionary items like holiday decorations, picture frames and small appliances. By comparison, Dollar Tree gets just under half its revenue from consumables.

The worry is that the discounters' core shoppers will be forced to scale back on those discretionary purchases. Fewer than 40% of analysts covering either stock rate it Buy or Overweight.