I had the same problem using a USB stick. The Media froze after playing a few minutes of a song. The Bluetooth streaming could be restored after a key-off period of time. However, whenever the USB was reinserted into the car, the Media lock-up re-occurred after playing a few seconds of music.
(I was not removing the stick when not used before the lockup. I removed after issue occurred.)
To fix the issue, I reformatted the USB stick and also renamed it to force the car to reread the contents of the stick. No issues yet, but it was only recently fixed.
It will be interesting to see if the issue happens again.