The agreement by President Biden and Donald J. Trump to move ahead with two presidential debates — and sideline the Commission on Presidential Debates — is a debilitating and potentially fatal blow to an institution that had once been a major arbiter in presidential politics.

But the roots of the commission’s decline go back at least a decade and came to a head in 2020, when the commission struggled to stage a debate with Mr. Trump and Mr. Biden during the pandemic.

The candidates’ first encounter that year was caustic and raucous, as Mr. Trump shouted over Mr. Biden and the moderator. “I’m a pro: I’ve never been through anything like this,” the moderator, Chris Wallace, said.

As it later turned out, Mr. Trump had a Covid diagnosis days before the event, leading to strong objections from the Biden campaign to the commission. The second debate was canceled by Mr. Trump after the commission sought to make it virtual because Mr. Trump was recovering from the illness. By the third debate, the commission gave the moderator a mute button to cut off a candidate who broke the rules.

But even before then, the commission has been on political thin ice. Anita Dunn, a longtime senior adviser to Mr. Biden, helped write a 2015 report that called for the debates to be updated for a modern media environment. Mr. Trump accused the nonpartisan commission, created by the leaders of the Democratic and Republican parties in 1987, of bias toward the Democrats. The Republican National Committee announced in 2022 that it would not work with the commission.

“The campaigns have always wanted to take the debates back for themselves,” said Alan Schroeder, a professor emeritus at the Northeastern University School of Journalism in Boston, who has written several books about presidential debates. “They have been trying for years to get rid of the commission. So we are back to the future with this and back to a future that didn’t work that well.”