Negative Inductance and Cascaded DC/DC Converter Instability

From your numbers it seems like the instantaneous draw when the audio output is at the maximum peak of the waveform is too much for converter 1. This would explain why it works at higher frequencies, since converter 1 then sees more the average rather than peak instantaneous current draw.

You say converter 1 puts out 12V at 1A, which is 12W. To put out 10W RMS audio power would mean the peaks of the audio waveforms draw twice that instantaneously. This would overload converter 1 by almost 2x according to your description. At 1kHz audio output, the overload happens for only about 250µs at a time. Since the average draw is OK, converter 1 doesn't fault.

This is just a guess, of course, but it is consistant with the information you provided.

I think your FAE is confused.

The amplifier is a constant-power load to the first DC-DC stage. If the first stage output voltage goes down, the amplifier will draw more current to maintain the same output power. The amplifier is therefore presenting a negative impedance characteristic, not a negative 'inductance' (whatever that means).

A negative impedance load does have implications for stability. If the magnitude of the negative impedance cancels out the power supply's output LC filter damping network, the power supply can oscillate.

Venable Industries has a series of papers on the topic of stability (H. Dean Venable = control system guru) - check out TP-12 (free registration required).

If you don't see signs of instability on the DC/DC stage (erratic pulses, sinusoidal ripple) then the premature shutdown isn't due to loop interactions.