WASHINGTON — When Sarah Huckabee Sanders, the White House press secretary, was turned away from a restaurant with her family over the weekend, conservatives across the country rallied to her defense, heaping abuse on the trendy farm-to-table spot for snubbing President Trump through his spokeswoman.

But one powerful voice in Ms. Sanders’s camp, Mr. Trump himself, took his time in offering his support to a top aide who has become one of the most recognizable lightning rods over his policies and false claims. He waited 48 hours before writing a Twitter post criticizing the appearance of the eatery’s exterior, which he called “filthy” and indicative of a “dirty” establishment. He called Ms. Sanders a “fine person.”

The episode — and the president’s uncharacteristically tepid, delayed response — pointed up a double-edged dynamic that seems to plague nearly everyone in Mr. Trump’s inner circle and has recently begun to take its toll on Ms. Sanders: Even as her vigorous defenses of the president’s misstatements and her own obfuscations during White House briefings have eroded her public credibility, her stock with Mr. Trump has begun to sink.

In recent days, Mr. Trump has asked people privately what they think of Ms. Sanders — an indication, they say, that the press-obsessed president has begun souring on her. He has also told her, before she heads out to the lectern in the briefing room, that he is “going to grade” her televised performances. (People who have heard Mr. Trump make the threat say it is in jest.)