Hello, I've been living with the Live Tile issues for quite some time. I never really looked into it until recently though. Thankfully, I was able to get them working again. I believe mine stopped working because I would install everything under the sun on my L920. I think that most apps with Live Tile capability default to enabling the Live Tile even if you don't pin the app to your start screen. With that said, I believe the OS has a limit of 15 apps with Live Tile enabled and when you exceed that count, the Live Tiles will break and or become intermittent. You can have Live Tiles enabled in an App and it will count towards the limit of 15 even though you may have that app blocked in Background Tasks. So the way I got mine working again was I went though and first uninstalled all the apps I never use. Then I went through each remaining app that was installed and disabled the Live Tile functionality within the App if I didn't need the Live Tile (I had already previously blocked most of the apps from Background Tasks). After restarting, my Live Tiles started working again. I currently use the following Live Tiles.
MetroTalk
Battery Pro+
Simple Calendar - I love this app!
Bing Finance
Bing Weather
Windows Phone Central - I've been opening the app like 20x per day looking for new news. Maybe now with my Live Tiles working, I won't have to open it so often!
Since fixing my Live Tiles, I've noticed that my battery life is actually better, even though I had ever single app blocked in Background Tasks before this. Before you say that my Live Tiles didn't work because I had them blocked, I need to say that I've tried enabling the Background Tasks for apps and they still didn't work so I just ended up keeping them all blocked. So now with a handful of apps non blocked and using Live Tiles I'm actually noticing better battery life.
Good luck to those with the issue. It wasn't fast and easy to get mine working, but now I'm happy I went through the trouble.