I seem to recall someone else having this issue a while ago. I think the solution was to keep the device active, eg. by playing silence. For example, you could create and play a silent sample like this...
BASS_Init(...); // initialize the output device of interest
HSAMPLE sample=BASS_SampleCreate(44100, 44100, 1, 1, BASS_SAMPLE_LOOP); // create a sample
BYTE data[44100]={0}; // a 44100 byte block of silence
BASS_SampleSetData(sample, data); // set the sample data
BASS_ChannelPlay(BASS_SampleGetChannel(sample, 0), 0); // play the sample
Please see the documentation for details on the aforementioned functions.