Auto-sync data turns itself off randomly On my Nexus 4, sync turns itself off randomly. 

Almost once a day, the option Settings > Data usage > Auto-sync data gets silently unchecked. My Nexus 4 is brand new, and I have not installed any apps that I think would interfere with system settings.

This is very annoying because I cannot rely on sync at all; I frequently miss important emails etc. Manual syncing is not an option.
I don't have an answer to that. I do have a workaround for it though.

Download this app from the play store called AutomateIt. It's an app that allows you to make the phones to respond to certain situations.

You could make a rule for the phone to follow, maybe something like: turn auto sync ON when screen is turned on.

Hope this helps.