Prevent opening new conversation

Hello !

I can't figure out how to prevent user to open new conversation when he come back on my website.

My website has a use that makes customers come back for several hours or even days to complete their initial conversation.

Currently, if I come back to the page the next day, I have the greetings message of a new conversation again. I would like to stop this until the conversation is completely closed.

I've tried increasing the "Conversation session timeout" setting to maximum but it doesn't change anything.

The "Auto-close conversations after a period of inactivity" setting is OFF

Is there another setting to configure this as I would like?

Thanks for your help :-)