Find a old drive and plug it in to the other SATA slot load windows on it and boot in to that drive then make a system image. That will tell you if it is the drive. I would be suspect of a company that can simply give you an answer "its not our fault its windows" did they do testing or did they just somehow know that by using the psychic troubleshooting method
You should open a new thread and post the exact issues you get. That way you can get an answer to the questions.
Does you shutdown only happen within the bitlocker login prompt or can you suspend bitlocker and recreate it. What are the time frame ranges it shuts down at? Are you getting a bitlocker recovery or a warning that you maybe at risk?
Bitlocker doesn't really have the ability to shut down and really the only thing that is running during the phase you are at is hardware. The rest of the system is at a pause.
You can create a USB unlock key and see if you get a crash when there is no user entered password required