Update:

I even tried uninstalling the plugin and reinstalling - and still nothing...

After experimenting with this, it appears only the creator of the event is unable to invite friends.  They can invite, but the users do not receive the invites on the site, the users only receive email notifications.

However, if the event allows participants to invite friends, they can - AND the users do receive those invites.

So, it appears that there is an issue with the creator side of things.

Creator can invite: but those invites are not sent via the site, only via email notifications...

If participants who manually joined the event invite users, users receive both the invites and the email notifications and all works as it should.

Any update on a fix?

Maybe there was a hiccup on the server side of things for a few days which caused a few plugins to not work.

Anyway, it's all good now.  Thanks for your response, and if it doesn't work again, I'll let you know and send you access!

Its really weird problem because it need to re-send invitations like 4 times and then it works but most of time just not!

www.mmoportal.eu/events

Now we know where the problem is, because when you create event as private you can invite only members who are online. I mean only online invited member will receive a notification about the invitation. I tried this with my 3 friends. 100% chance on this bug on my site!