There are usually two battery supplies to a radio. One via the ignition for running the radio. The other as a permanent feed for the radio memory etc. so it might be the ignition feed failing/failed ...possibly a dodgy connection , loose fuse etc
Check with a multi-meter or test lamp.
see
http://www.tehnomagazin.com/Auto-radio-car-connector/KENWOOD-Car-Radio-Wiring-Connector.htm
RegWorts
August 2008
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