Originally Posted by MVPS
it should be working 24/7. An "offline livechat" will create the opposite effect.
It does not have to be on 24/7. it is just another support channel where a customer or potential customer can chat with a live person.
Some larger companies actually use bots and virtual assistants to run live chat sessions.
showing you are offline is not negative as it shows you are real, people do expect live chat not to be running 24/7, some live chats systems will make live chat links invisible if no one is online.