One reason IBM could make the transition from electromechanical (not analog) systems to programmable computers is that it wasn't really a disruptive change to their business model or to their customers. They were still renting out punched-card business machines. On the other hand, the switch to digital cameras totally messed up Kodak's film-based business model.
Another factor is that both Thomas Watson Sr. and Jr. were very strong, effective leaders for IBM (based on what I've read and heard).
Another factor is that both Thomas Watson Sr. and Jr. were very strong, effective leaders for IBM (based on what I've read and heard).