What you also need to remember is that the battery that provides you with electricity in the air, in case of an alternator failure, is the same battery that also runs the starter motor. Sometimes for at least five minutes or so, in case of a pilot who seriously gets his priming or startup sequence wrong. (I have witnessed a pilot attempting a start for 20 minutes with the fuel selector closed...
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The first sign of a weak battery will probably be that you can't start the aircraft anymore in cold conditions. How weak the battery needs to be to fail starting the engine, and how much juice can then still be extracted from it at low loads, probably differs from battery to battery and airframe to airframe. My gut feeling says that if you have no problem starting the engine, even if you mishandled the priming a bit, then the battery should have enough life left in it for a low load, for at least 30 minutes. But I'm no battery expert and I'm interested to hear opinions on this.