No, these were straightforward unbalanced TS patch cables.
That said, that should make no difference whatsoever. In fact, even if I'd had all outputs and the master volume cranked to all-100, all the time, using unbalanced cables, and then used them in a nude photoshoot with a bondage fetishist and a dozen ferrets, it should make no difference because those are outputs, and they carry no voltages except those generated internally. (And no, I didn't plug them to each other, or any other outputs.)
If the sockets themselves are failing, that is sad, but should be a (relatively) easy fix. If the problem is (speculating here) a capacitor or a transistor dying internally, chances are that's because of a faulty batch from a manufacturer.
The behaviour of the system suggests that there is some input volume (i.e. voltage) beneath which no audio signal is generated. This could be because of a dodgy contact inside the socket itself, although that would be unusual, but is more likely to be something like an internal noise filter going bad somehow in the DAC.
My best guess is that there's a piece of electronics near the socket that is not wearing well, and this is the root cause. My surmise is that this is owing to a subcomponent manufacturing defect, and that Akai, once they nail this cause to the wall, will be exercising the kind of penalty contract best compared to a rubber glove, a tub of vaseline, and a manic cackle.
I hope then that in the interests of their customers, they issue a general recall.
Sex spreads disease, drugs poison the brain, but rock is still safe.