We can't manually configure chat messages to refresh for the end-user. If someone sends us a message and we solve their problem, there's no way to manually make the chat history clean up/mark it as resolved so they can send us another message. This looks and feels very clunky for the end-user.
The six-hour auto-refresh isn't perfect because conversations can take longer than 6 hours (which would force the chat visitor to restart a chat on the same issue). The chat visitor could also return in under 6 hours in which they can't start a new conversation.
Hey there! Have you enabled the option to end chats and refresh automatically in Front Chat channel settings? You can read more about this in our help documentation here.