Managed to ‘fix’ the 10016′ error, although all that did was suppress the warning in event viewer. That was a red herring.
Today I changed the supplied USB 2.0 extension cable to a USB 3.0 one and connected it to the ASMedia 3.1 controller – and it worked fine. No disconnects.
Swapped back over to the Intel USB 3.0 controller and it’s still working fine. No disconnects.
The only other change I made was in the device manager:
> Intel(R) USB 3.0 eXstensible Host Controller>Properties>Power Management> untick ‘Allow the computer to turn this device off to save power’
Perhaps it was a bandwidth issue all along causing the disconnects.