Occasionally a colloquy on a post will prompt a commenter to move the discussion to chat, as recently happened to me. The chat room thereby created: is it persistent, or does it expire after some time?
Rooms with any sort of meaningful content exist forever.
As outlined in the chat FAQ, "A room is considered worth retaining if it has more than 15 messages by at least 2 users." Any such room is available for everyone (including non site members) to find on this list of RPG.SE chat rooms, for as long as the Stack exists. Also they're seeded to Google.
The original Question/Answer page doesn't automatically get a link to that chat room, because anything productive to improving the main site content should be applied via edits to the questions and answers. The chat is there to reduce the clutter so questions and answers are easily found, not to add to the reading someone needs to do to get a good answer.