It could also be a wiring fault in the radio's "keep alive memory" circuit.
An automotive radio actually has two power leads - one is a low-current lead that is "always hot," which serves to keep the memory (presets, clock, and suchlike) in the radio ticking over. The drain caused by this lead is nominal - a few milliamperes, or so. And, a "switched" or "hot in RUN" power lead - that's the one that provides power when you turn the radio on to listen to it.
Since a middlin-charged nine-volt battery is enough to keep radio memory alive and keep clocks going, I'm more ready to think "wiring fault" or possible "radio fault" than "battery going flat" - especially since you don't mention starting difficulties or slow cranking (you'd think it was an unrelated symptom of some other problem, but you'd be surprised at how often disparate problems in a vehicle can be interrelated...)
Oh - but it's not really a "short" - a "short circuit" is a fault where the wiring bypasses the load, and allows full source current to flow (which blows fuses.) What you are probably fighting with is an "intermittent open" - which can be all the more irritating, because looking for a short circuit means you're probably looking for the wrong thing...