I have partner flights booked using Avios for which I never ever received the emails. Most flights I get something at some point - perhaps a bit delayed in order to account for the lag from reservation to ticketing.
But I did have a few LAN flights I booked earlier this year that, although ticketed (and visible on BA.com, and flown) simply never arrived via email. I only just remembered this today as I was trying to pull up the cost of these flights for accounting reasons. Not a trace in email.
I can find the miles in my BA statements, and I can find the charges in my AmEx statements, but unlike almost all my other bookings, I can't find any email from BA.