I am having this problem on my xperia Z2 too, where the Calendar keep notifying how it had stopped working.
My issue was persistent and not random
I was not going to go through the hassle of a factory reset as suggested by Sony.
What I did was, for all calendar related apps(calendar, calendar storage, Sony's Calendar which runs off google calendar)
1) Stop all process for the related apps
2) Stop all cache process for the related apps
3) clear cache and data of all for the related apps
4) Uninstall Calendar.
5) Install Calendar from Playstore
6) The newly installed calendar will require you to sign up new or existing account, click "Not Now".
7) Go to Accounts, under Google, uncheck calendar sync and check it again to re-sync to the new calendar.
So far starting calendar has no error.