Apps constantly disconnecting from the internet

I've got a new phone running Android 4.4.2 and whenever I close an app, it disconnects, i.e whenever I close Messenger, it stops being connected to my WiFi so I get no notifications until I open the app, when it reconnects and everything comes through. All apps are doing this, on WiFi and on data. I can't find anywhere to manage background internet usage and was just wondering if there's a (probably very simple) way to sort it out?