To all those who gave me suggestions regarding my mic detection problem.
Thank you for all insight, and I will try all suggestions, but I fear the problem might stem directly from the fact that I am using kX drivers, which are pretty non-standard by their nature (albeit it's the only driver that allows me to manipulate and duplicate output as I see fit).
I did let RS access the internet during install however, especially since I did the same on my laptop and mic detection works fine there (please note; on my laptop I have the same OS, firewall and such; the audio drivers are of course different however).
I also read suggestions to try and rename the mic in the Windows sound settings to something that contains the word 'microphone'. No dice. Someone also suggested renaming the default playback device to 'line 1', but this ended with similar results.
Please remember, that I CAN get RS to detect my voice; if I disable speech recognition before starting a lesson and then re-enabling it when it's already in progress then everything works fine. It's just that the silly app cannot detect the mic when it starts a lesson, and thus causes problems.