First thing's first. This is on Linux Mint Debian Edition with Cinnamon.

I've been having this problem for a while and mostly ignoring it until it gets really annoying and then restarting the affected program to clear it up. What happens is that my sound works fine for a while but then gets very stuttery. This happens mostly in games and in Mixxx.

Today I finally got sick of it and got down to some troubleshooting. I found this in the logs:

[92022.877595] usb 7-4: reset high-speed USB device number 4 using ehci-pci

That's repeated several thousand times. As you may have guessed further investigation determined that usb 7-4 is my headset (a wireless Logitech headset). So...there's that. But now I'm stuck. Does anyone have any idea what my next step should be? The logs don't give me any clues as to why the headset is being reset, but it's apparently happening several times a second once it starts.

how does it work when you disconnect the headset?

That's something I hadn't thought to try. I just did though. When it started stuttering I unplugged the headset and Pulse switched over to a dummy output. I switched it to the onboard sound. I couldn't hear it because I don't have any speakers or headphones with a 1/8" plug, but looking at the applications tab it was still flickering back and forth. Interestingly when I plugged the USB headset back in and switched Pulse back over to it the problem stopped and didn't come back while I was playing my game. That was only a half hour or so, but I'm taking it for a good sign.

ok.
that was confusing.
what application tab?
and 1/8"? is that a small headphone plug (3.5mm)? you don't have anything that would go in there?

maybe your system doesn't like to boot with the headset plugged in? that would be some sort of usb receiver, like for a wireless mouse, right?
if that is the case, one could probably create a udev rule or something to not take any action regarding it, during boot time.