Something that happens only once per year is going to be very hard to track down. There are no internal events which happen at that frequency. And I’m sure that the server is rebooted more often than that.
My first guess would be that it’s a user event that is causing it. Some sort of massive database query that takes a couple of days to run, and is only run once per year.
Unforunately I’d need to look into the system and get a lot more information before being able to provide you with any real direction.