While Nvidia has remained quiet about the fault, but it seems that the issue is with the power adapter cable (rather than the GPUs or the 12VHPWR connector).
Igor Wallossek of the German-language hardware site Igor's Lab found that the adapter, which is apparently manufactured by a company called Astron and was provided by Nvidia to all of its board partners, uses "a total of four thick 14AWG wires distributed over a total of six contacts," with a thin solder base that Wallossek says can be damaged easily when the cables are moved or bent.
The solder inside of Nvidia's power adapter cable can be damaged if the cables are moved or bent too much.
"If, in the worst case, the two outer wires break off, the entire current in the middle flows through the remaining two wires. The fact that this then becomes really hot does not have to be explained separately."
Contrast Nvidia's adapter cable to the 12VHPWR cable provided with a Be Quiet! Dark Power Pro 13 power supply, one of a few newer ATX 3.0 PSU models with a 12VHPWR cable that connects right to the PSU rather than relying on an adapter. The cable is thicker than the one in Nvidia's adapter because every pin has its own wire, but it also runs cool and delivers reliable power to the GPU.
Wallossek also said that Nvidia told its partners to send all affected cards back to Nvidia for further investigation and testing.