Notifications are shown as
Sent in BA providers control panel, but the customers (or the specific ones) state they do not receive it.
Check what mail server is used:
Make sure the host set processes e-mails correctly.
For example, if you see
[Server] Host = localhost Port = 25
that means that local mail server is used to send the notifications, check /var/log/maillog on the BA application server to check the notifications sending status.