Is it normal for the battery to drain while leaving one of these plugged in? In just one night.

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My 12v sockets disconnect power after a short time, with the "key off". Look at some of the threads here about battery problems and see if you fit that issue.
Larry

 

It is not normal. I've had for the 1.5 years that I've owned it with no issues at all.

 

I have a charger + battery pack in the cubby so my phone is always charging when connected even when the car is off, outlets themselves are powered down and no issues.

You probably have the dreaded power mgt issue or simply a bad battery.

 

What is the dreaded power management problem? And can it be fixed? Just had battery fixed and it was fine -

 

Many threads about it. Connecting to ODB port causes failure. Cure most of the time is to disconnected battery to clear errors and reconnect.