The accessory battery is very small. Once it has been flattened a couple of times it will not hold it's charge and needs replacing. All that testing of a high powered amp that draws a lot of current for such a small battery will not of helped.
You don't say how old the battery is, but most need replacing within 5 years.
Once replaced, don't turn on the amp until you have started the Twizy so the 12v battery can be recharged from the traction battery.