@Chelle1 Sometimes those notifications glitch out and stop working. You can first try unchecking your notification preferences and then rechecking them, which may reset things. But I stopped receiving text notifications at one point, and it took a month for them to get it fixed.
It's a good idea to check multiple ways you want to receive notifications, i.e. SMS and email, so in case one glitches out, the other may still function. In the meantime, you may have to use the desktop version if it's the app you're having problems with. And check your message Inbox a couple times a day so you don't miss any inquiries, requests, reservations or guest messages.
And contact Airbnb to let them know about your issue.