I tend to run into this problem myself but have figured out some creative solutions to keep it as interesting as I can. To me it really starts with the game. Is the game visually interesting enough to warrant silence as stuff is running around on screen? Can you show what's on screen without worrying about a copyright claim? If you can answer yes to one or both then you being a visual storyteller you won't need interesting commentary throughout those sections.
Now for me I personally film/record about 1 hour 1/2 to 2 hours of footage per video and then cut them up to 18-35 minute videos at most. That way I can decide what stays and what gets cut. So if there is silence, bad commentary, something inappropriate that was said, interruptions or anything else that might ruin the video/audio I can just cut it.
Lastly the worst I've had was there was nothing to talk about a game during live recording that was interesting throughout. Too much silence. For those I was thinking post-commentary would be better from all the players together since we won't be as tired or focused when watching it back.
Those are just a few of my solutions to help with the commentary issue. But they don't apply for live streaming either. Hope that helps regardless and best of luck. =]