In laymans terms, what they're saying is happening is that your BAT phono preamp is just letting straight DC current go through the circuit and into the speakers... just like when you hook a battery directly up to a wire connected to both of it's terminals, (try it sometime if you haven't done this) what they're proposing is the straight DC current just fried the voice coils...
It's possible that a tube is arcing or something, possibly damaged from vibration or shock during shipping, and a trip back to the manufacturer might provide the easiest way to correct the situation... aside from something happening with a tube which would affect the output voltage, other factors involved could be a leaking capacitor, the resistence of the IC's that you're using with the unit, and a couple of other theories like the subsonic or ultrasonic oscillation (feedback) theories that have been proposed in the threads which would show up on a scope while the music was playing, but otherwise wouldn't be heard at all...
with a DC offset problem, there would not be any excessive speaker excursion necessarily, as what would be happening is when music is being played, along with the source signal some straight DC current would be passed into the speaker as well, so when no music is playing the speakers would be fine... however, when music was playing the speakers would start to heat up... a DC offset problem, or voltage leakage, results in the speakers heating up and the voice coils melting....
if you've got speakers that have brass plugs in the center, like the SEAS Scanspeaks, you can actually touch the center cone and feel whether it heats up at all while the music is playing... but from what you're describing, it does sound like the symptoms you would get if the voice coils were getting fried... as the voice coils overheat, they begin melting the wax they're embedded in and they begin losing their perfectly round and symetrical shape... as the wax continues to melt, the coils start to separate from the wax which holds them in place, and when the wax has bubbled and melted enough, the speaker ceases to function... so at first you notice the sound "drop off" as the wax starts melting, and then... no sound... just a blown speaker... best thing would be to have the manufacturer check the unit and hope they can find the problem...
If you do want to experiment with the unit to check for speaker excursion, or to feel if it's heating up because of a DC voltage leak being sent into the voice coils, just limit the playing time to around 30 seconds or so... this is enough time to make whatever checks you may want to... but it's not long enough for the wax to melt should it be a problem with DC voltage being sent directly into the speakers...