I'll bet that's it- I believe that SX's default clock rate is 48kHz. When it gets confused about its clock input reference, it switches back to that rate until it can sync up again. So if you have a project that's recorded at 44.1kHz, it'll play back morphed up to a higher pitch *while SX is confused*. Not quite double, but still wrong as hell, and pretty upsetting....
There's a mismatch in the settings of the reference clock source, and muting those busses must glitch that source for long enough for SX to get confused and fall back to the default. When I've done this, I've always seen it recover in very short order (2-3 seconds max- before I can do anything else), but that's with a Hammerfall set for word clock in, not a Mona set for internal clock as the reference. The driver software probably has a lot to do with this recovery time. SX should pop up a dialog box telling you that the default clock rate has changed, when this happens.
At any rate, I swap output busses continually without ever experiencing this: I use the busses as direct outs and fx sends to external analog gear, and reconfigure them many times per session.
I know nothing about the Mona or its software. This'll probably piss Jim off, but you'll need to check the manuals to make sure that the clocking is configured correctly on the sound card itself, and check once more to see that you have the latest/greatest drivers. If the drivers are good and SX and the Mona *agree* on who is the master clock source, I can't see any reason for this to be happening.
This is one of the reasons that I went with a central word clock generator- so that I could set _everything_ to a single, stable, external reference. There are so many interactions between drivers, Cubase, Windows, and everything else that I just solved it by using the big hammer.
All this probably doesn't help you, but there you go. My advice is worth exactly what you paid for it, anyway!