New Delhi, July 23 -- A large services company was on the verge of losing one of its oldest clients. Months of patient relationship-building had begun to unravel after a series of operational lapses. As the situation deteriorated, the leadership team reached a familiar conclusion. There was one executive they wanted involved immediately.

She was neither the account owner, nor the most senior person in the business. Yet everyone knew that if anyone could steady the relationship and persuade the client to stay, it was her.

Within weeks, the account had stabilized. A month later, another troubled client surfaced. Once again, her name was the first to be mentioned. Then came a struggling project. A newly promoted manager needed mentoring. A...