My non-Gmail address ("NGA") is the backup for my Gmail account. It also forwards messages to my Gmail to keep things in one place.
The other day, I logged into Gmail, and a login warning/notification was sent to my NGA.
But when my NGA tried to forward the Gmail notification to my Gmail account, Gmail rejected it.
Luckily, the Postmaster message to my NGA notifying me of this failure was successfully forwarded from my NGA to my Gmail account, which I had just logged into.

