This has been an issue for me as well. Being at work and constantly being signed out of O365 is horrible. I have a small work around that helped me though When you need dumb luck try this It is super simple and was done by accident and may not work for everyone. I have been opening O365 in Chrome. I just opened 2 of my Outlook tabs and for some reason it ...
There seem to be native HTML5 desktop notifications working for Outlook web now, but only under Windows. It's not there for Linux, which is really strange given it's the same API. Not sure why they chose not to support it under Linux given that's really the only missing piece for critical feature parity in the browser.
I would suggest you follow these 3 simple steps:
Import (instead of just subscribing) your Google Calendar to the Outlook Web Application.
Use this "Google/Outlook Calendar Sync Tool" excellent applet to sync your calendars.