When do the icebreaker messages reset?

The icebreakers reset in a staggered manner starting from the day you send the first icebreaker. 

E.g. If on January 1st you send your first 10 icebreakers, 30 days later the tracker adds 10 back, and so on. They *do not* reset all at once on the 1st of each month or every 30 days.