Aggregate Device + Rig Kontrol = Broken

Symptom: I put Native Instruments' pedal board Rig Kontrol 3 into an aggregate device with the Built-in Mic, Built-in Input, and Built-in Outputs, and the output degrades to crap. It sounds fine at first, but it's just a matter of time before it degrades into either a mass of digital static followed by silence or, on rare and special occasions, several seconds of latency. Resetting the buffer size resets it, until it breaks again. And again. And again.

Is it a problem with Rig Kontrol? No. First, if I select the RigKontrol3 device itself and accept the output from the RK3's headphone jack, the sound doesn't degrade. (I'm learning to play that way, but it still feels weird having my headphones plugged into something on the floor.) Second, even when I'm using the aggregate device as I want it set up, the input runs all right, as I discovered one editing session when the sound crapped out on me. It's the output from the aggie that contains all the distortion, and that means it's happening inside the computer.

Can I fix it by setting Drift Correction on the Rig Kontrol? No; I've tried that a few times.

Is it a problem with using a USB1.1 device? No; not only does the Rig Kontrol 3 work fine by itself, but it is a USB 2 device plugged into the "high-speed USB" bus (verified through System Report.

Can anyone please suggest any other courses of action, or is anyone else having a similar problem? Better yet, did someone else have this problem until someone suggested a fix?

(Also, feature request: Could we please get the ability to rename inputs and outputs on an aggregate device so they look less generic? It would take the guesswork out of using an aggie with a lot of devices in it. But bigger problems first, please.)