I fixed this nuisance years ago after the switch in my radio failed and
I had to buy a new one.  Simply install a DPDT (double pole, double
throw) rocker switch somewhere, I put mine in the dash next to the
radio.  Hook up the hot wire to one side of the switch, and the ignition
switched wire to the other, then hook the radio power wire to both of
the other poles. Then you can use the switch to turn the radio on and
off when the ignition is off.

--
Stuart MacMillan
Seattle

'84 Vanagon Westfalia
'65 MGB (Driven since 1969)
'74 MGB GT (Restoring)

Assisting on Restoration:
'72 MGB GT (Daughter's)
'64 MGB (Son's)

Parts cars:
'68 & '73 MGB, '67 MGB GT