have had what I think is similar issue.... on both ipad and iphone. Running IOS6. Have gmail account setup through exchange connector. IOS receives and accepts invites just fine from external devices.... If i create a new invite on the IOS device and add invitees with external email addresses, once this calendar invite is saved into the diary it doesnt trigger invites to go out to those 3rd parties... but the invite definitely is in the calendar as can also see it on mast google calendar.
If I then go and move the timing of the invite that has been created on the IOS device (by holding down and dragging to new time) this then immediately triggers an invite (new Invitiation, not reschedule) to be sent to the external email addresses... any further modification to timing of invite then triggers 'reschedule' calendar invites to go out - so expected behaviour.
The issue is that IOS is not triggering the invite to go out to external parties who have been added to a newly created invite - and it only does this when the date/time of the invite is modified.
Spent about 1.5 hrs on phone to apple support yesterday - they have now passed on to 3rd level support....
Are others seeing the same behaviour as above?