Sears’s bankruptcy filing was supposed to give the troubled retailer a fresh start. But a year later, the chain is still struggling with many of the same problems it faced before it sought court protection.

Roughly a quarter of the 425 Sears and Kmart stores that financier Edward Lampert bought out of bankruptcy have closed or are closing, according to people familiar with the situation, a retreat the chains haven’t fully disclosed.

The shelves at some remaining locations are bare of crucial products—no lawn mowers in summer or garden supplies in spring, according to shoppers and a former executive.

“It was hard to find anything to buy,” said Edgar Dworsky, a consumer advocate, who recently visited a Sears in Saugus, Mass., but had trouble spending $10 in loyalty rewards. He settled on a DieHard flashlight, because the Everlast sneakers he wanted were out of stock.

Sears ruled for decades as the nation’s largest retailer, filling American homes with appliances and anchoring suburban malls. It was undone by its own missteps, the rise of new competitors and the shift to online shopping. Under the 14-year stewardship of Mr. Lampert, who was at various points chairman and chief executive of parent Sears Holdings Corp. , it slashed spending with little investment in stores.