I recently discovered I had this issue. I volunteer for a non-profite charity and had set up meetings with several (dozens) of new clients and also a co-worker for several different meetings during the month of Jan 2017. I sent invites to each client and my co-worker. I sat there fat dumb and happy thinking they all got the invites as I got not bounced emails nor error messages. It was't until a week later that I learned that NONE of the invites went out. So, I started doing some trouble shooting and even called Apple support. Initially, it seems as if I could send an invite as long as I did not include a location or other additional info, however as time went on the problem progressed (why I have no idea) so that now, I can't send ANY invites - even if I include NO additional info such as notes or location. In other words, my Calendar is completely useless to me for setting up important meetings.
I have been in contact with Apple Care and even got sent to a senior tech, who has since sent this to the engineers. I read on a different forum that this is a KNOWN BUG that Apple is working on. In my humble opinion, if Apple is aware of this bug they should let ALL iCloud users know about it. This is not a trivial bug. Imagine someone setting up a meeting where life or death is involved or some meeting where a huge amount of money os involved? This bug could have very real and very severe consequences. It is unacceptable that Apple did not tell me of this if it is a known bug. They could be setting themselves up for HUGE lawsuit if this bug causes some serious consequences, and they knew about it.