I was really disappointed when my new Nexus 5X did not sync new e-mails and calendar entries from the web. I use these functions all day long and the device is useless if it does not update new items. I already began to install 3rd party apps, but then decided to look into the matter again: It seems to be a known bug that Google is investigating, but I couldn't wait for them to come up with a fix. I suspected the cause to be the Android 6 doze function (a battery saving function in Android 6) since my device hadn't updated the calendar for several hours (I could see that my account/calendar was last updated the night before at around 9 p.m.). To disable the calendar's (and a few other apps, but I suspect that the settings for the calendar is enough) battery save function use the settings: (The screenshots are in Danish, but I think you get the point)