No chat is ever deleted. They stay in the inbox or archive forever. The only way a chat can disappear for a user is if it's a group chat and the user is removed from it or leaves it, but even then the chat still exists for the other members of the group chat.
Think of chats as messages; once it has been sent you can keep or archive your copy of the message, but the message that exists in the recipient's inbox will always stay there (or could be archived by the recipient).
To organise your inbox and create greater visibility of important chat messages, use the Archiving Chats function.