My battery woes are now gone thanks to the full reset of my phone. I'm now able to use Facebook just fine. I'm not sure what was causing the rapid Facebook drain, but after toying with my phone I was able to get satisfactory results. Wish you all the best of luck.
Best way to get rid of your battery issue with iOS: wipe your phone clean.
A complied list of all of the battery optimizations:
1. Reset your network settings
2. Turn off your Bluetooth radio
3. Avoid enabling Push and Fetch mail on Exchange accounts, although this might be counter-intuitive (what's the point of having a smartphone if you have to turn it off?)
4. Selectively turn off Location Services and turn off all system services Location Services features.
5a. Selectively turn off applications you don't need to be notified of that use Notifications.
5b. Turn off Weather and Stock notifications. I've never seen anyone I know ever need this.
6. Avoid downloading apps that you're not using or will constantly poll and activate GPS
7. Turn off Diagnostics and Usage in General > About
8. Add a Restriction to iTunes and Ping (if you're not using these services)
9. Avoid turning on GPS-enabled Reminders when you have Exchange accounts.
10. Turn off iPod Equalizer (Music EQ)
11. Turn off Spotlight features you're not using
12. Turn off Push features that your applications may be using that you don't need.
For granular battery optimization,
12. Turn off vibration.
13. Turn on Automatic Brightness
14. Use Airplane Mode where there's no reception.
15. Adjust the Auto-Lock so your screen is not constantly on.
16. When you're not using your phone, turn off your screen.
17. Avoid spamming Facebook... It's not because I hate Facebook, but the app is poorly designed. If you constantly refresh your Facebook or leave it in an infinite loop of loading pictures or notifications Facebook will continue polling the server for data. Out of most of my normal apps that are not supposed to be battery intensive, Facebook and Messenger seem to drain my battery the most.
For battery maintenance, run your phone down to 0% and charge it to 100% while its off, run it down to 0% again, and charge it while its on. Keep your phone in normal room temperatures (no extreme heat or cold) and avoid dropping your phone.
Although my battery life is far from optimal, I'm at 20% right now from a full charge and I'm getting 13h standby and 6h of usage. Not so shabby for iOS 5. I used to get insane numbers on 4.3.5 though, going almost 1d on Standby and 7h of usage, but I'm not asking for more.
Wish you all the best of luck!
-dimgl