I had a similar experience with an American Jeep Grand Cherokee .. .. .. .
The problem was caused by the power block on the back of the ignition switch. When the car was started from cold as the key is released the ignition barrel springs back to the 'run' position which makes contact for the various ancillaries including the radio.
When cold the power block made contact OK, but once it had warmed a little, maybe with some arcing, if the key was turned off and then on again, it made contact perhaps 50% of the time and a bump in the road would sometimes affect it.
Of course, it affected other things apart from the radio, but unless they were on at the time, they were not so noticeable.
S