Yes, your Rabbit chat history is saved automatically for private Direct Messages.
Your chat history is saved temporarily in Room chats. The Room chat history is visible to all guests in a room, unless the chat has been cleared by the room owner.
Check it out: How do I clear my chat history?
Does Rabbit monitor my chats?
We do not monitor or read everything that happens in Rabbit (we're a small team!). But we do have tools that flag bad behavior, images, and illegal content to our staff as they're posted in real-time. If content shared is reported, flagged, and/or deemed as illegal, we are required by law to report it to law enforcement agencies.
You can help: If you see something inappropriate or illegal, report it. We want Rabbit to be a fun and inviting place to hang out, and as much as we can, will work with the rest of our community to keep it that way.