I am not from Laminar Research,just a flight simmer from down under.
You will not get an answer in this forum from Laminar.. As you have already done, I was going to suggest you contact Laminar direct. Have you tried making contact through firstname.lastname@example.org?
When running the digital version of X-Plane you need to ensure you are connected to the internet at all times. The software performs a silent check to ensure you are running a legal copy all the time and also not running a duplicate copy at the same time.
I also understand that even though you have applied the product key to give you the full legal version and able to run the software without being connected to the internet, the software will attempt to perform the silent check. It will remember the number of disconnects and will eventually shut you down.
Good luck in getting your key recovered.