As of couple of weeks ago it seems, for myself and those I share calendars with at least, that a new issue developing regarding calendar invitations and also the inconsistent way shared events are displayed in shared calendars...
I strongly suspect this more than coincides with some backroom activity going on at Apple regards addressing the recently highlighted issue of spam calendar invitations but so far those I have spoken to deny this.
Problems I have currently:
When create a new event in MY calendar and INVITE my partner she no longer receives an INVITATION ALERT. Even more strangely, examining her calendar "inbox" reveals the invite has already been filed in the REPLIED section and with the status ACCEPT! (it seems iCloud is automatically accepting invites on her behalf...). However... the event is NOT displayed in her own calendar at all. Meanwhile, my own copy of the event in my calendar shows her invite status as "NO REPLY". This is completely bizarre and also works the opposite way - eg if my partner is trying to invite myself to an event. This all used to work fine, albeit with occasional delays In propagating the calendar event data to all of our devices.
I have tried unsubscribing each other's calendars and starting again with regards inviting one another to share our respectvie calendars - no change.
Have also done the usual switching off of iCloud calendars on these devices, deleting locally stored calendar data and switching back on iCloud sync. Again, no improvement. I have found the issue extends also to another party I sometimes invite and who also has a long established iCloud account.
Our iCloud accounts are definitely linked to our Apple ID email addresses so no scope for error there - or so I thought... Another recent, lengthy telecon with Apple Support found me being advised to make sure we both had @icloud.com email addresses added to our contact details wiin the contacts app. I cannot believe this is a requirement and besides we never needed that before.