I have no idea.
How old are these conversations? There might be a time limit involved. Is it possible the conversations are from before the board software switch?
cereal_killer might be able to answer.
Thanks for the prompt response.

I really appreciate that more than you know. Lol. I believe I am going to let this go . . . for the time being, but if CK wants to come here and give me some information, that would be appreciated too.
Here is the actual solution to your question
When you create a conversation, you can check a box that allows anyone in that conversation to invite others, if the person who created that thread did NOT check that box, then no you can't invite others as a participant.
So, sometimes you have conversations where you can invite others even though you didn't create the conversation, and sometimes you don't.