Windows 7 and/or some of the audio device drivers have a useful set of settings.
For example, the "Supported formats".
I have my device connected to an old Roland VM-3100Pro mixer which only supports 44.1kHz sampling rate PCM. So, I selected the following :
I thought this was sufficient to get sound working. I was wrong.
Despite my choices, Windows and Realtek had automatically selected the following "Default format" :
Notice that the 48 kHz rate. Never mind that I didn't select that in the "Supported formats". This should not happen. Windows should never pick a format that's been marked as unsupported.