On my FP (second run) the mobile data turns itself off from time to time.
I need to walk dowi into the settings menu to reenable it, the icon on the network overview screen does not work in this state.
The same seems to happen to Bluetooth as well, we’ll have to confirm that.
This happened to me once after setting up caldav synchronization with ownCloud. Do you use DAVdroid / synchronize you calendar / contacts?
Late reply - sorry. Only Google Calender so far - does it use CalDav?
The problem still persists but is not as annoying as other problems…
I don’t know what Google uses… I suggest a hard reset, if you are also having other troubles.