After 10 years of hosting, I've just started experiencing this problem recently. It began with two situations where prospective guests contacted me and I received a normal email notification. I replied and they did as well, but I did not get a notification (via email or my phone) that they had replied. It was just sort of luck that I saw there were messages. Then after I accepted the reservations, the notifications started rolling in normally.
Today I received a booking request and responded to it. Then this evening I started getting Airbnb texts and emails telling me it was the last chance to respond. I thought that was odd since I'd already responded and then noticed I had three other inquiries that I hadn't received any notice of!
This isn't an email problem. I also didn't get notices through the app nor did I get notices through SMS (which I guess is a new thing this month).
I informed Airbnb support the first time I dealt with this but as is often the case these days, they were rather useless. Has anybody else experienced this? It's not realistic for me to check my Airbnb account every hour to see if there are new messages.