It almost sounds like the sub might be going into thermal protection. Either that or you are clipping the input signal. It probably isn't due to the newer cable. The calibration may have caused the AVR to send a larger signal to the sub that is either overloading its input stage or running the sub so hard that it enters self-shutdown to avoid over-heating.
By the way, none of these parts are worth taking into a paid repair service, the repair is likely to cost more than just buying a new unit. I think the solution may end up being just needing to get a more powerful sub. One way to test if the input signal is clipping the sub inputs is to lower the LFE output in the AVR (maybe by 8 dB or so), then play something at a high volume on the AVR and see what happens. Alternatively, you could just raise the gain knob on the sub itself and rerun the calibration.
However, if the problem is the sub is going into thermal protection, you are going to need a bigger sub, since that one cant handle how hard you are pushing it.