peregrine
If you get the same issue with a second AI, I would pull the power supply and check it,
assuming you have a meter, or take it to a shop for a bench check. It could easily be
giving you the noise you're seeing. For a replacement, your specs indicate you could
operate perfectly well with less than half of that 1200w beast, unless you have a really
insane video card.

A meter (assuming you mean a multimeter) is not going to be all that good at determining the presence of very short spikes. It would be useful primarily for testing voltages, which could well be nominal and still produce the symptom. An oscilloscope and some patience might be useful in this context. 
 
I would go a step further than cactus music and suggest that you move your interface to another computer in a completely different building. Things like a neon sign or a sparking capacitor in a motor some distance from your usual work area might be at fault. Of course if changing the interface solves the problem you are done.
 
The fact that the symptom resolved after the system was turned off for a period may be significant. If it happens every time it suggests something is warming up (expanding?) and then commencing a problem. A loose connection or leaky capacitor in the system might be at fault.

I use multiface 2 with sonar platinum.  I have to disable the onboard sound card. in device manager (actually I wrote a quick batch file that enables the on board sound card and reboots if I want to listen to youtube.  and another one that disables the on board sound and reboots to run Sonar).
 
have to have separate speakers for onboard sound card and mulitface 2(sonar). 
 
 
When using SONAR I also disable the network adapter in control panel.  I also disable AVG antivirus.  
 
the multi face does direct monitoring so I don't have to fart around with input monitoring in SONAR. So when recording vocals, I click the master in the RME mix software which represents the headphone out and I bring up the top row (hardware input) of faders on the input that has the mic plugged in.  This gives me the sound coming out of the DAW  AND the immediate hardware input monitoring of the singer so they can hear themselves. 
 
Here is my point.  If the faders along the top row (make sure you click the little wrench in case a track is hidden in the stereo mode) are up you will get noise from those inputs added to the the output.  
 
So select the different outputs you have setup (main, monitor etc.)  at the bottom right and make sure all your individual faders along the top row in RME mix software are off. 
 
(If you nave not checked this). 

David - here's where I'm going with this. If a different brand/model AI works, this is solved.
 
If a different AI is not available, and RME support doesn't have an answer for him, I would
check voltages on the PSU. If they're out of spec, I'd replace the PSU. If the problem persists,
and is limited to the audio from the MultifaceII, then the highest probability is its arising from
the power supply on the PCI card. Then we're back to getting a new AI. Again, I'm assuming
RME support has him confirming he has sync lock, done cable checks, etc.
 
 

papacucku: 
 
It's good you came and posted, especially since you're using Windows 7, just as the OP.
 
Are you using an ASIO driver with your Multiface II, and are you running x64 Win 7?
 
If so on both counts, maybe you can zip the Multiface II drivers package (you installed to get the ASIO drivers in SONAR) and send it to the OP some how. He says he's using a WDM driver, and he's saying he doesn't see any ASIO inputs/outputs in the Audio Devices section of the Unified Preferences View. If the driver package he installed has ASIO drivers, he should see the ASIO inputs/outputs when he sets SONAR to use ASIO driver mode in the Unified Preferences View. I think you can be a big help to him helping him out here.