As the managing partner of a top Los Angeles law firm, Norman H. Levine is no stranger to what might be called the Posada problem.

Nothing, he said, is as tough as telling fellow partners that their best days are behind them. “I’ve always joked that I wish I could have these conversations by phone,” Mr. Levine said. “If someone wants to stay and you don’t want them to, that’s the hardest. It’s like going to your parents and telling them they can’t handle their affairs anymore.”

If anyone doubts the sensitivity of the task, consider the case of Jorge Posada, the once-formidable New York Yankee who at the ripe old age of 39 found himself demoted in the starting lineup, unable to consistently do the one thing a designated hitter does — hit. When he got the news earlier this month, he walked into manager Joe Girardi’s office an hour before the game was to start and announced he wasn’t going to play.

Few professionals in other fields have that option — Posada’s contract guarantees him $13.1 million this year, despite a batting average of .183, the lowest among designated hitters in Major League Baseball. But the painful encounter between coach and lagging star — Posada apologized the next day — is one that is taking place with increasing frequency in the wood-paneled aeries of law firms, banks and other elite professions, industry insiders said.