My Modi3 is 2.5 years old and stopped being recognized by my PC a couple of weeks ago. Schiit were polite and professional but couldn't suggest anything beyond sending them the DAC (on the other side of the planet) for repair at my own expense., which wouldn't have made sense for me financially.
I didn't see this thread at the time, but immediately bought a Topping D10s locally. I figured that if only the USB receiver had failed then the spdif inputs should still work and I could test this with the D10s' digital output. And if the whole thing had died, then I had a ready-made replacement.
Sure enough, little Modi3 works perfectly when fed through an optic fiber. To my uncontrolled, subjective ears - and with absolutely no quantitative evidence in support of this opinion - Modi3 sounds marginally nicer than the D10s, so I've ordered a Sky Song USB-SPDIF converter and will use the Topping in another system.
Regarding the source of this seemingly common problem: my guess is a systematic defect in the chip. It sounds like the hairdryer treatment is thermally activating carriers in the channel of a bad transistor within some type of latching circuit, thus explaining why a single brief dose of heat is sufficient to fix the problem until the power is cut. But I haven't worked on silicon since I was an undergrad so am very happy to be corrected here.