I am once again able to send 15 introductions with my business account after archiving received introductions that were marked with a status of "Pending".
Here's what happened: I complained to LinkedIn customer service that although my list of sent introductions said that I only had eight introductions "In Process", my "Accounts & Settings" page told me that I had 0 of 15 introductions available to me.
I got a response from LinkedIn customer service that I needed to withdraw all pending introductions in both my sent and received introductions inbox. This didn't make any sense to me because all of the received introductions marked as "Pending" did not offer me an option to withdraw, because the details showed that each received introduction had already been accepted or rejected. So the only options I had for these received introductions were to archive or, in some cases, reply to the introduction. So I archived all of the received introductions marked as "Pending" and amazingly, I was then able to send additional introductions until I reached my full 15 introduction limit of sent "In Process" introductions.