This has been an issue for me for a little while now and I'm not entirely sure if it's just me.
I play on Steam and have the checkbox enabled in game which should allow social notifications when playing etc.
I've no idea if people are inviting me unless I make a conscious effort to keep opening the friends list during training.
Edit: The same applies for me when in game - not just training.
Edit edit: Invites are there waiting. It's the notifications that don't work until you leave training / the match.
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