Clock does not turn off! 1997 Blazer

I don't drive the Blazer very often, so it sits a while between excursions. When I go to use it, the (new) battery is dead or almost dead. At night I noticed teh clock and radio stay on! Although I am able to power the radio off, the clock still remains on. Is this an ignition swich problem? Thank you in advance...

Factory original radio or aftermarket?

It is the stock, factory radio/CD unit. Nothing has been changed on this vehicle, it just started doing this.

In the instrument panel fuse block, remove the radio fuse. it should be a 10 amp fuse in the #24 position. Make sure the ignition switch is in the OFF position and that the radio and clock are off. If the radio fuse is not in the #24 position, check your owners manual for its location. Post your results.

Well I removed the fuse, clock is definitely off

There are two fuses labled "RDO": one is for the radio, which will also illuminate the clock, and the circuit only has battery voltage with the ignition in the ACC or RUN positions. The other fuse has battery voltage at all times and it's for the station memories and the clock memory. If you're certain you removed the radio and NOT the memory fuse, the next step is check voltage at the ignition switch.