Outlook on android - receiving notifications, but emails don't show in inbox.

I simply switched to 

Edison Mail+ android. Far better app 

Isn't that a paid app? 
Does it fully integrate with Office 365? Calendars and appointments, the whole works? 

I hate the thought of paying for an app when I pay for the Office 365 subscription. I think an App or a suitable mobile web access should be included, but at this point I'd be willing to consider overlooking Edison mails privacy practices for a consistently working email app.

It's pretty sad that this issue has been around for five years and it appears that no engineering has been done to remedy it. I have been through all the remediation steps, reset account, delete / add account, delete / add app, full background permission and it still doesn't seem to be working. Is there something on the server side that is causing this?

As far as I can tell the issue seems to reside in the app on the phone, or rather how it interacts with Android and other apps on the phone (maybe), there doesn't seem to be any server involvement. 

For me, I've found that if everything is not fully up to date, things start breaking more quickly.

Outlook and Authenticator and any other MS linked apps can't be allowed to go to sleep. (Battery optimization has to be off - if everything is up to date, you won't have a choice, optimization won't be available)

The other thing I've noticed is that the older your device, the less chance you have of it working (probably directly related to updates). I have a Pixel 2 that it doesn't work well on and an Android 10 generic chinese phone that the app consistently does not work on. Probably because Blackview is definitely not on top their updates for the phone. Oddly enough I had issues with an iPhone 11 Pro too, before the 12 was out, so It's not Android specific. Or wasn't for a long while. Now I got a newer samsung phone and it *seems* to be working well again.

I too think it's a shame that Microsoft isn't fixing it... from what I read elsewhere, or maybe even earlier in this thread, MS doesn't make the app, they bought it. IMO they overpaid, like I did for every phone made since the Galaxy 6 series. We all have been overpaying the hardware they're pushing out, while they continue to neglect actually fixing the software bugs.

I simply switched to 

Edison Mail+ android. Far better app

We use Workspace One UEM (Airwatch)  - Msft responded and asked me to turn off Battery Optimization for Outlook and Intune.  ( i had previously only turned it off for Outlook)  But so far this is working for me.    -  Im not sure if you can enable the setting to turn off battery optimization for those apps, but they need to be able to stay alive in the background to pull mail so when you tap notifications, the mail is there.  

https://docs.microsoft.com/en-us/exchange/clients-and-mobile-in-exchange-online/outlook-for-ios-and-android/outlook-for-ios-and-android-faq#q-what-does-background-synchronization-enable-i-notice-that-when-i-launch-the-app-with-it-enabled-i-still-have-to-wait-for-messages-to-download-even-after-ive-received-new-mail-notifications-for-them-and-sometimes-i-get-reminders-for-appointments-that-had-been-canceled

I have been sending diagnostic logs to MSFT.  They said for my particular issue, Battery Optimization has to be OFF for both Company Portal and Outlook.   (Tap notifications for new email, no email is displayed anywhere in Inbox)  I have several android devices, Pixels, Samsung Note/Galaxy devices.  It was only happening on my Pixel device.  But I have other users experiencing this on Samsung.  I cannot turn ON battery optimization to reproduce the issue on my other devices.  See this article, its part of their FAQs:  https://docs.microsoft.com/en-us/exchange/clients-and-mobile-in-exchange-online/outlook-for-ios-and-android/outlook-for-ios-and-android-faq#q-what-does-background-synchronization-enable-i-notice-that-when-i-launch-the-app-with-it-enabled-i-still-have-to-wait-for-messages-to-download-even-after-ive-received-new-mail-notifications-for-them-and-sometimes-i-get-reminders-for-appointments-that-had-been-canceled

For your particular issue, I would recommend opening a case if possible, if you have followed the steps in this article and try uploading Diagnostic logs to the MS case so they can examine your logs.