I'm not sure if long running sockets are allowed on mobile phones these days. They were pretty normal for a couple of years, but phone battery life has increase

I'm not sure if long running sockets are allowed on mobile phones these days. They were pretty normal for a couple of years, but phone battery life has increased substantially since Apple and Google started streamlining the notification system and basically sleeping background services that would otherwise poll for notifications through sockets. You'll still get your notifications, but (hours) late. You may instead want to pcap a mobile client to see where the notification is coming from, I bet the server still phones home somehow. It's possible Apple exempted themselves from their notification policies and integrated their Exchange push services into the OS power manager like they did their APN service, but I'm not sure if I'd expect them to put in that much work for what's essentially a competitor. As a side note, because it's not made clear during setup: the Outlook app for mobile phones will keep a copy of your email on Microsoft's servers (and a partial copy on the device); if you use that app, Microsoft will poll for updates the normal way and likely still push the notifications through Apple's servers, despite you not having set up any direct connection from your server to the cloud. This isn't the case for the built-in email clients, of course, but the Outlook app seems to be quite popular for Exchange accounts.