Share your experience!
Even if Stamina mode is off, the intenet(Data connection) seems to be disconnected,The notifications from facebook and whatsapp pour in only after screen is on.I repeat the stamina mode os OFF.
Do you have any taskiller, task manager, antivirus, battery apps, is it through wifi or data ?
Do the apps work on wifi? If so see if background data for all apps is enabled. Settings--Data usage--menu--Restrict background data. And also check the options for individual apps. Settings--Datausage--select the app--see if restrict background data is enabled.