I had the same issue and it got progressivelu worse. Orginally, when I plugged the FIOS DVR into the Xbox One every now and then mainly when I switched to my WDTV on my stereo the Xbox One would lose connection and I had to reboot my FIOS DVR to get it to recognize. This was annoying but I could deal with it.
But once the Olympics started the FIOS would freeze for 5-10 seconds every minute and would do it on the DVR as well. This is strange since the FIOS DVR is connected up stream from the Xbox or My Stereo...I know HDMI is a two way connection but strange.
So I started to chat with Verizon and they sent me a new FIOS DVR...and when I asked about Xbox One support they did not know. They immediately told me ai had a Bad DVR and sent a recycled one....once I took the Xbox One out of the loop the problems went away...
When I got the new/recycled DVR I had a minor issue which I resolved, but when I asked about Xbox One Support for the FIOS DVR I was told they were not compatable....
I have not hooked the new DVR to the Xbox One Yet...
Is anyone else out there using the FIOS DVR connected through the Xbox One and not having issues?