The RME Interface works on 8.1 (including RME TotalMix software). It's the additional software - DigiCheck - which does not.
I'm not suggesting that NOTHING works in 8.1. I'm just throwing out caution. I was also surprised after I posted a month ago on the RME Forums that the latest version of DigiCheck (out 6-Aug-2013 or so) doesn't fix the problem. I suspect that within that window an RME developer replicated the issue on 8.1 to see if there was an easy fix.
I'm totally prepared to believe it's the RME Software that is the problem. I'm just sharing information in case I can save someone trouble.
I would also not be surprised that Sonar (which is tightly coupled with Windows) isn't having any problems with some Windows change where other companies (RME and who knows who else) may have a problem.