It has been decades since there was any real uncertainty at the top of the Republican Party in the Senate. But Senator Mitch McConnell’s alarming freeze-up at a news conference on Wednesday at the Capitol, as well as new disclosures about other recent falls, have shaken his colleagues and intensified quiet discussion about how long he can stay in his position as minority leader, and whether change is coming at the top.

For months even before he had an apparent medical episode on camera on Wednesday while speaking to the press, Mr. McConnell, the long-serving Republican leader from Kentucky, has been weakened, both physically and politically. The latest incident made those issues glaringly apparent: Mr. McConnell, 81, froze mid-remarks, unable to continue speaking, and appeared disoriented with his mouth shut as his aides and colleagues led him gently away.

Senator John Thune of South Dakota, the No. 2 Republican, quickly stepped in behind the lectern and picked up where Mr. McConnell had left off, in a scene that underscored how the lanky 62-year-old has positioned himself as the leader’s most obvious successor. It was a reminder that no one — even Mr. McConnell, who this year became the longest-serving Senate leader in history — is irreplaceable and raised questions about how long Mr. McConnell could continue to simply gut it out.

Months ago, there seemed to be a developing race to succeed him among Mr. Thune, Senator John Barrasso of Wyoming, the No. 3 Republican, and Senator John Cornyn of Texas, the former whip; they are known around the Capitol as “the three Johns.” But during Mr. McConnell’s extended absence earlier this year following a serious fall, Mr. Thune moved into the position of taking charge of the conference.

Mr. McConnell had a concussion in March when he fell at a Washington hotel during a fund-raising event, and was absent from the Senate for weeks while giving almost no updates on his health status. Since then, he has had at least two more falls, one at a Washington airport and one in Helsinki, during an official trip to meet the Finnish president. His office disclosed neither, and has stayed mum about his medical condition on Wednesday after the episode, which some physicians who viewed video of it said could have been a mini stroke or partial seizure.

Mr. McConnell, who had polio as a child, often has trouble with stairs and has long walked with a wobbly, uneven gait. But in recent months, he has been using a wheelchair to get around at the airport, which a spokesman said was “simply a prudent and precautionary measure in a crowded area.”

His diminished state has been evident in his role in the Capitol as well. Some of his Senate colleagues were surprised at the back-seat role he took throughout the debt ceiling negotiations, where he did little and left Senator Chuck Schumer, the majority leader, and Speaker Kevin McCarthy in charge. The old McConnell, they said, would have not stayed on the sidelines, and many Senate Republicans were ultimately unhappy with the outcome.

Last year, Mr. McConnell weathered a rare challenge to his leadership when Senator Rick Scott, Republican of Florida, decided to oppose him and received 10 votes. In the past, Mr. McConnell has been named leader with no contest.

Senator Josh Hawley, Republican of Missouri, who voted for Mr. Scott, declined on Thursday to comment on Mr. McConnell’s health, but he said that he still wants new Republican leadership in the Senate.

“I have never commented about a senator’s health, whether it’s Senator Feinstein or Senator Fetterman, so I’m not going to do that with Senator McConnell,” Mr. Hawley said. “I voted for different leadership, and I stand by that. My preference would be for different leadership, but that doesn’t have anything to do with his health.”

Dianne Feinstein, Democrat of California, is 90, in frail health and with memory issues that make it difficult for her to function alone in the Senate. On Thursday, her colleague Senator Patty Murray of Washington had to help her when she appeared to be confused about a vote on a military spending bill. “Just say aye,” Ms. Murray told her, as she began a muddled speech.

John Fetterman, Democrat of Pennsylvania, who had a stroke during his campaign and uses a closed-caption device to help him communicate, was absent from the Senate for six weeks earlier this year while being treated for clinical depression at Walter Reed Military Medical Center.

Mr. McConnell is also a survivor. He pushed through childhood disease to rise to the top, maintained his iron grip on power despite a constant barrage of attacks from former President Donald J. Trump, and has never been willing to show any sign of weakness or entertain any challenge to his leadership of the Republican conference. Mr. McConnell’s position of power in Washington for decades has also fueled an entire network of operatives whose livelihoods are tied to his staying in his current position.

Since the unsettling episode on Wednesday, Mr. McConnell has been trying to give the impression that he is fine. His aides will not say whether he consulted with a physician after the incident. Unlike the president, who is required to release a detailed, annual physical, senators are not required to reveal anything about their health. Mr. McConnell, aware that showing any vulnerability triggers questions about his power, has always been more closed-mouth about his health than most.

On Thursday, his colleagues continued to rally around him.

“Mitch McConnell is the leader; he’s a strong leader,” Mr. Barrasso said. “I was with him last night, he gave a wonderful speech. He’s 100 percent with it.”

Senator Mitt Romney, Republican of Utah, said that he had spoken with Mr. McConnell, whom he described as “fine.”

“He will continue to lead the party,” Mr. Romney said. “I don’t anticipate any change.”

Senator Roger Marshall, Republican of Kansas, described Mr. McConnell as “large and in charge of our lunches: He’s still playing four-dimensional chess up here when it comes to politics.”

Hours after his episode on Wednesday, Mr. McConnell attended a reception hosted by Major League Baseball, where he heralded the innovation of the pitch clock, but made it clear that he doesn’t intend to be on one himself.

“It’s no secret that I’m a conservative and an institutionalist,” Mr. McConnell told the crowd of baseball enthusiasts. “I’m always more inclined to preserve institutions that work as they were intended. After all, in my line of work, rule changes can mean tossing out important protections for the minority.”

He added: “I’d hate to see legislation governed by a pitch clock. But a neat nine innings in two and a half hours? That’s something we can all get behind.”

Senator Joe Manchin, Democrat of West Virginia, who attended the dinner, said the appearance made him hopeful about Mr. McConnell’s health status.

“He spoke last night, he sounded good,” Mr. Manchin said. “I’m praying to God everything is good.”

On Thursday, Mr. McConnell spoke on the Senate floor, making no mention of the jarring incident and instead giving a diatribe against President Biden’s military budget request. Later in the day, he was set to meet with the Italian prime minister.

Kayla Guo contributed reporting.