It sounds like a momentary issue with your Internet modem. If it's an all-in-one device (Internet/phone/WiFi), it would cause a complete outage.
Swap again to duplicate.
How is the "stuttering" box connected to the Internet...wired or wireless? There are a few things to troubleshoot without relocating equipment. You could use a wired connection, increase its QoS on the router, swap the HDMI cables, review the video settings on the TV. etc. If you still can't correct the stuttering, exchange the box.
Bruce: No, it's not an all-in-one device. I have a cable modem and a phone modem but all of my services went out concurrently. The "stuttering" is associated with my Contour 2 main device and it's coax-attached..and it only happens when I'm watching Netflix through the Contour app. The video has the appearance of having dropped/frozen frames; the motion is not smooth. I also have a satellite Contour box on my other TV and I don't have any Netflix problems with that box. That's why I wanted to swap them to see if the problem follows the box. The TV associated with the "stuttering" Contour 2 box is a Samsung Smart TV which is Wifi connected to my home network. It's built-in Netflix app doesn't have any stuttering issues whatsoever but there's a known issue with my TV and the Samsung sound bar and Netflix which causes the sound to drop every once in a while. So I get to choose between dropped sound or dropped video frames. I'll try swapping the boxes again; if it causes another outage (I don't think it will, but) I'll have the answer to my question. Others have posted about this same problem in the Cox forums (stuttering) so I know it's not just me.