You can close a dialogue at any time. Closing a dialogue stops the dialogue and removes it from your current list of dialogues. That is, closed dialogues do not appear on this page.
You will be able to view closed dialogues but you can not add to them. However, closed dialogues are eventually deleted and after that point they obviously will not be available even for viewing.
If you do close this dialogue, then you will have to start a new dialogue if you want to continue to "talk" with this person. That person will re-appear in the list of people you can start dialogues with.