Battery life is very subjective & depends on a lot of factors like the following:

1) Data network 2G/3G
2) Amount of background tasks you enabled
3) No of live tiles that refresh every 30 mins
4) Signal strength

If you're on 3G data, expect short battery life especially if signal strength is not at max. So I'm usually on 2G data except when in places where 2G signal strength is bad & 3G signal is better. A good eg, my office room. 

WP8 actually limits the no of background tasks you can run to a max of 15 which is great. But if you have 15 apps running & updating live tiles, then yeah you'll suffer more when it comes to battery life. Remember, this only affects apps you specifically enabled in background tasks. I have a lot of apps pinned to my start screen but I only let 10 update it's live tiles.

Finally, signal strength. I find phones nowadays are very sensitive to this. I noticed this when I was using a Nokia N9 since Jan 2012. Have data enabled & not have good signal strength will kill battery quite fast. For eg, I can kill my N9 with 3G data enabled in around 4 hrs inside my office room, doing nothing much. My Lumia 920 fared slightly better, managed an hour more at 5 hrs. But at home where signal strength is at max, I can even leave data enabled on my Lumia 920, as battery draining is not much when idle.
You can try uninstall & reinstall the app affected. That fixed some of my notifications issue when I had them. Most are just misbehaving apps. Like for eg, the official Twitter apps notification always works but FB one is hit & miss, no matter what I try. Another thing to look out for is the max no of background apps. You might have hit the max no of 15 without realising it then WP8 go block the app from running. Just a suggestion.