The phrase "unending conversation" is correct and usable in written English.
It can be used to describe a dialogue or discussion that seems to go on indefinitely or without conclusion.
Example: "Their unending conversation about philosophy lasted well into the night, leaving everyone else in the room feeling exhausted."
Alternatives: "endless dialogue" or "ceaseless discussion."
Just days earlier, she had visited Danny's Facebook page, which is itself an unending conversation.
Although he spent just six months in his father's unusual household, Alan, we come to realize, has kept up an unending conversation with these ghosts from the past.
Jewish culture, consolidated through Halakha, the religious Jewish legal tradition, created a civilization that has devoted itself to an unending conversation among different viewpoints and the coexistence of contradictory attitudes toward the fulfillment of the good.
Social construction of knowledge is something we're accustomed to seeing in political and social contexts; it's the root of Burke's "unending conversation" metaphor (Burke).
Dave Hudgens, the Mets' hitting coach, said that Bay was a batter who relied on "rhythm" and "feel" and that their unending conversations about hitting were now tailored to that fact.
For all that has been made of Senator John McCain's accessibility during this campaign season and how the Arizona Republican has used his "Straight Talk Express" bus to hold unending conversations with his traveling press entourage, Mr. Gore's campaign operation provides a vivid counterpoint.
The mainstream left and right, he felt, had got it wrong by concentrating on results, especially material results, while ignoring public virtues such as civility, courage and what Oakeshott called "conversation"—the unending exchange of ideas among people of different beliefs and opinions.Summarising Oakeshott in this way is bound to make him sound a hothouse English plant.
Mother's Day is an unending atrocity of bland conversations, many of which feature clearly dubbed-in lines to make sure the most unsophisticated audiences never get lost.
Conversation with him was an unending delight, a voyage of discovery with a continual frisson of ideas and insights.
After an engaging conversation with yet another of Marjorie Agosin's seemingly unending stream of cousins, it was approaching two o'clock and we hadn't eaten lunch.
Sprawling medley of unending malls If you mute all mechanical noises in this city you'll hear conversations in different languages, usually had over meals.
