Why does my battery drain when the unit is powered off?

I have a Surface Pro 4. This is already my third unit; the first two were replaced free of charge because of battery issues. The first was draining too quickly and the second shut off unexpectedly once, refused to charge and never powered on again.

Now, this unit has a different battery issue:

The battery depletes when powered off! For example, I can have it charged to 100%, power it off and less than a week later, it will fail to power on without being plugged in, because the battery has been completely depleted.

I’m fully shutting it off - not just in power save mode or hibernating. None of my Google searches have led me anywhere.

Unfortunately, the unit is no longer under warranty. I took it to The Microsoft store and a ‘technician’s” solution was for me to purchase a brand new newer model and get credit for my unit.

Are their any solutions to this?

Thanks