During one of her regular Sears shopping sprees, Kyra Dwyer picked out $150 of clothes for herself and her daughter. She was charged $18.

The 47-year-old is a member of Shop Your Way, Sears’s loyalty program. She regularly stopped at the store near her home in Fairfield, Conn., until it closed in January, on her way home from her work for the Coast Guard. She scooped up Craftsman tools, Lee jeans and a snowblower for her parents. Nearly all of the items were paid for with rewards points.

Fewer...