I don' t mean to speak for anyone, but the hosting club seems to have the most effect on the speed at which the invitations are received. My club held its first ever qualifier. I sent the score sheets to the IBO within two days of the event. The IBO sent the invitations 10 days later, including mail time. The day I received the invitations they were mailed to the recipient: total time was two weeks from the shoot to the delivery of the invitations.
I know individuals who attended a qualifier on april 27 who have yet to receive their invitations, though they know they qualified.
So, I can say from my experience that whatever delay you are experiencing, it is likely with the host, not the IBO itself - they are quite efficient.