I had this happen, I suddenly stopped getting booking confirmation and review notifications by email. However all others (messages, reminders and enquiries were coming through fine), also all notifications were coming through as alerts to my phone via the APP fine so fortunately I was at least being made aware of new bookings.
I contacted support and predictably got the advice to check my spam settings etc etc - but I do not use any spam filters in my email client. I then created another email address on my domain and changed my registered email address on my AirBNB account to that one which did not solve anything.
I then changed my registered email address to a gmail email address I set up and everything started coming through fine which told me that AirBNBs emails were being blocked by my ISP. Sure enough I contacted my ISP who confirmed the emails from AirBNB been flagged as a source of spam and were being blocked at ISP level.
Looking at the email message headers the booking notification emails do have slightly different headers to the emails which are coming through including the return address which I think may be the issue if a spamming company has been inserting airBNB's email details into their spam which of course AirBNB could not be aware of or do anything about.
I don't know what the spam filter ISPs use is (Spamcop, Spamhaus or something else) but AirBNB need to first acknowldge they are being spoofed and then contact the ISP level spam filter to get the block on their genuine emails lifted.
