So after having tried the digital clock screensaver the problem still occurs. My sense is that the digital clock screensaver in comparison to animated full screen saver doesn't use as much memory and lasts a little longer.
I don't know where the "paused tv buffer" is saved but assuming it's on the Roku it could only hold so much and eventually craps out. if you've saved what you are watching it shouldn't be an issue because that would be done by the app provider ie Youtube and it should beable to restart where you paused because the entire show is saved.
I've not verified the saved show theory to see if it works but if it does the work around is to save the show you're watching.
Hope this helps.