LONDON—Elon Musk’s Space Exploration Technologies Corp. may lose a spacecraft launch order from a major customer, Inmarsat PLC, even as the European satellite operator voiced confidence in the rocket company’s ability to return to flight this year.

SpaceX, as the rocket company is named, lost one of its Falcon 9 rockets in an explosion during a routine refueling exercise in September at Cape Canaveral Air Force Station in Florida. It destroyed an Israeli satellite Facebook Inc. planned to use to provide internet access to...