Mitch McConnell

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.”