The chants, led by Democrats, broke out early on: “Where’s Mitch? Where’s Mitch?”

Republicans quickly shouted over the ruckus. But the repeated nods to Senator Mitch McConnell and his absence at the political stump in western Kentucky reflected how much his recent hospitalization and the sparse, limited official statements about his recovery have gripped Kentucky politics.

Mr. McConnell has been a fixture at the event over the last four decades, as he helped grow Kentucky’s Republican presence into a dominating political power. But he has not been seen in public since he was hospitalized in mid-June, fueling questions about his health and whether he would return to the Senate before his term ends on Jan. 3.

“I hate that I’ll miss the fun this year,” Mr. McConnell, 84, said in a statement announcing his decision, adding that “there’s no place I’d rather be on the first Saturday in August than with the good people of western Kentucky.”

However, it has also become the raucous opening number to the state’s fall political season, giving candidates and elected officials a chance to throw out gibes, roasts and one-liners to a heckling, cheering crowd. (No onstage profanity or audience-held noisemakers, please.)

Mr. McConnell, who attended at least 30 picnics as he climbed the Senate’s leadership ladder, helped elevate the picnic into the national spotlight. In his statement this week — as he has before — he gloated that it was no longer a lonely place to be Republican.

This Saturday’s event would have been Mr. McConnell’s last as senator, given that he is retiring, and the transition to the next generation was underway. Andy Barr, who won the Republican primary to replace Mr. McConnell, said he spoke to the senator on Friday and he “is looking forward to getting back to work in the Senate very, very soon.”

It was still disappointing to some, however, that Mr. McConnell could not attend his final picnic as senator. Brief tributes to his health challenges and service were met with rousing applause and at least one standing ovation from Republicans.

“If he could get released, he wouldn’t go to the Senate — he would come home and he would make his way to Fancy Farm,” Steven Elder, the event’s political chairman, said of Mr. McConnell.

“I am sad that he won’t be there to throw punches — I’m sad he won’t be there to receive punches,” he added in an interview before the event. “He loved it.”

Punches, indeed, were thrown, though not at all were aimed at Mr. McConnell.

In response to the recurring “Where’s Mitch?” chants, Republicans shot back with taunts about the absence of the state’s Democratic governor, Andy Beshear, his travels across the country and the rampant speculation that he might run for president. (Mr. Beshear told reporters he was at his son’s last high school travel baseball tournament.)

The absence of Mr. McConnell from work in the Senate does remain complicated for some Republicans. There is an undeniable frustration with an aging Congress and entrenched incumbency, with some voters believing that he should have already retired from office.

And some acknowledged that they thought Mr. McConnell and his staff could do more to provide information, beyond the two photos his office has shared.

Those around Mr. McConnell “should have been more transparent about what was wrong with him, what happened to him,” said Dan Albers, 68, as he finished a cup of butter pecan ice cream. But at the same time, Mr. Albers added, “I wish they would leave him alone.”

There were others who also thought Mr. McConnell’s history of surviving polio — something the Office of the Attending Physician has said remains “a significant factor in his mobility” — and his political legacy warranted some grace.

“We understand why Mitch declined,” said Catherine Brooke, 64, who came from nearby Paducah, Ky. She added that she hoped people would “remember everything he’s done for Kentucky.”

“They know he was retiring — why can’t they be respectful?” said Tammy Elliott, 64, who came to support Mr. Barr, Representative James Comer and the Republicans. She added, “We miss him this year.”

For some Fancy Farm families, the politics serve as a sideshow to a beloved tradition akin to a reunion. But it was strange, some said, to not see any “Team Mitch” signs on the roads winding into town or hear his supporters as they worked a shift at the barbecue pits, the concession stands or the bingo tables.

“Small-town America is the nosiest bunch of people you’ll ever meet,” said Carilynn Coombs, 38, chuckling as she stood in the meat stand her family has worked for decades.

“We care about everybody,” she added, “so we just want to know.”