Rudy, could the presence of the battery lower the threshold of required voltage to shutdown? Obviously, without a battery of any kind, below around 5 volts, the sound cuts out. Also, with a battery, just a stray leakage voltage might be enough to trigger it. I didn't have a lot of luck simulating that, but every RS board is somewhat unique due to component tolerances, maybe some have that narrow band of uncertainty?
Just a thought...