Batteries should not be looked at in isolation. They are half of the electrical system the other half is the alternator (or generator in older planes). You can get a good start from a fully charged battery but if the charging system is not on line you are quickly going to run out of power as its charge is depleted.
That is why checking the ammeter is an important after start, preflight, and in flight check.
If the charging system fails in flight the battery will be supplying all the electrical loads. As it is depleted the voltage will drop. The first thing to go will be the transponder as it needs full voltage, so if you are flying along and ATC suddenly says that they are no longer seeing your transponder return one thing to consider is that this might be the first sign of electrical problems. Of course as soon as the charging system goes off line the ammeter will show a discharge so if you regularly scan the instruments you should pick up the problem early.
As the previous poster me mentioned, if you deplete the battery starting the engine the radios will not work at idle power because the battery doesn't have enough volts but the RPM is too low for the alternator to provide the power. If you get stuck in this position increasing the RPM to 1500 should provide enough juice to get the radio on line. This however is not a great practice.
If I get a start off a weak battery I always stay at idle and watch the ammeter. It should show an initial high rate of charge which after a few minutes should start to reduce. If the charge rate stays very high then you have battery and/or charging issues and you should get an engineer to look at the aircraft .
