As normal user (i.e. without VIP status), you can send one Icebreaker per day. After it has been sent, the Icebreaker refills within 24 hours - this means you have a new one the next day.
As a VIP, you get three Icebreakers per day. As soon as you send one of these, it regenerates in the course of eight hours. When you send more than one, they do not regenerate simultaneously, but one at a time. Each Icebreaker needs eight hours, until it is ready again. When you send all three in a very short time, then it takes 24 hours until you can send another Icebreaker.
You can, however, buy additional Icebreaker messages. They will only be accessed, once your regular Icebreakers are used up. This means there's no need to panic, when you see your soul mate in the app and don't have any Icebreakers left.