Radio shuts off on it's own after 20 min./and clock inop.

[Consonar]

Bought a 2004 X5, 3.0i w/155K. Beautiful car but has issues. I've been correcting one by one.
My issue is the AM/FM radio isn't tied to the ignition key. It's always hot. You have to manually turn on and off.
When on, it will turn off after 20 mins on it's own. If you press the volume/on/off button it will come back on for another 20 mins.
And unable to set the clock on the radio. I had the LED strip replaced.
Also the number 73 or 74 10a fuse in the back (for the radio) seems to have a short. Every time I a new one in it blows the fuse (only took me three to learn something is wrong). Apologies for incorrect post in a different thread. Just finding my way here at Xoutpost.