Same here. I had it for months in a OnePlus3 (oxygen OS). And suddenly stopped showing the emails. It shows the notification, but it is not able to download the message to the inbox. Only works when within my working network. The problem is for the working email only (webmail.XXX.XXX). The personal account (very old hotmail account) works OK.
I tried all the stuff indicated above and does not work. I could only re-link the webmail account when back at work. Once back home, stopped working again. I suppose tomorrow morning will work again when at work.
The solving sync problems thread (going to the web, devices, remove, etc) does not work either.
Unable to download apps from Play Store using mobile data. For MIUI 8(previous versions also). Check your 'Security' app's - Data usage - Restrict data usage - System tab. Within system check Downloads is allowed to use Mobile data. Here's how to download Google Play Store and install the latest version on your device! Gets frequent updates, which is great news. The not-so-great news is that it can take weeks, or for some.
Also considering moving away from outlook if not solved soon.
In my computer (also with outlook manager; windows 10) works OK at home.
Android Not Downloading App Updates Free
I have started to have exactly the same problem as Leocadio Blanco-Bercial. It is very frustrating - the app has worked perfectly for months and just recently has stopped downloading emails when away from work (despite me receiving notifications of new emails).