Hi,
I don’t see why that would work for some users and not for other users :/
Could it be that you have some custom code (filters/hooks) for the notifications?
Also, is user P… having a valid email?
Do you see any different behaviour if using SMTP or the mail function from PHP?
Are notifications enabled for that user? Is he the author of the private content which should trigger a notification?
Our add-on is basically using the wp_mail function, that is rather simple and straightforward.