I, too have been experiencing the following...
1. Messages for reservations and inquiries come in, but the AIrbnb app does not show a badge
3. Messages are delayed sometimes by minutes, sometimes by hours showing up inthe Airbnb app, while
SMS texts and emails for those messages arrive fine and in a timely manner
I spent a bunch of time on the phone with Apple AND Airbnb and neither solved my issue.
Obviously all my settings are set to ON for notifications, but still nothing.
So, what do we do now?!