I have been using the system with Ubuntu 16.04 and 18.04 LTS for a few months without incident. After rebooting after a few days of not using the system I booted up to discover to drive detected. I have confirmed on another system that the drive is in working order and I even installed a new drive without remedy. I have attempted to reset the bios defaults and upgraded the BIOS with BE0077.bio using the jumper method. BIOS upgrade went smoothly but my issue remains. I was also using the TPM (PTT) but I have since cleared it also.
Are you actually seeing the M.2 SSD within the BIOS Setup screens? If not, I might suggest that you reinstall the latest BIOS, but this time do so using the BIOS Recovery process (documented here: Intel NUC BIOS Update and Recovery Instructions).
Hhmmm... If it is not showing up in BIOS, this pushes the issue into the hardware realm, unfortunately. Either the SSD or the M.2 socket is not working properly.
The problem probably is in the NUC. In the first you mentioned that this SSD was successfully tested on other system, while other SSD wasn't worked as well on this NUC. So, I suggest that you should open a request for RMA in order to replace this NUC: https://supporttickets.intel.com/warrantyinfo?lang=en-US
