Since the DuRec recording is free of the noise, it's pretty clear that the issue is either with the connection between the UFX and the computer, or within Reaper itself.

Because its occurrence is intermittent, troubleshooting will be lengthy and tedious, but you may get lucky. The first step would be to swap out USB/FW cables to see if the fault lies there, or to try the "other" connection (if using USB, try Firewire - or vice versa), as the fault might be not the cable, but with either (or both of) the UFX's or the computer's connection point(s). If that is the case, you will need to have the offending hardware repaired.

The last place to look would be Reaper itself - could there be something causing it to lose sync with the incoming sample clock? Some other software which momentarily interrupts Reapers connection to the computer's audio hardware? You might want to try increasing the amount of processing latency used by the UFX, which you should be able to adjust within Reaper. Yes, you'll hear your incoming audio with more of a delay than what is happening in the room, but at least you won't have signal degradation.

A last thought - the quasi-rhythmic nature of the interfering sound reminds me of what can happen when a cel-phone is used in the vicinity of a recording device. You might try placing one right on top of your UFX and/or your computer to see if you can re-create the interference that way.