Is your Facebook App up to date. Older versions of Facebook App have been reported to be buggy, if not noticed by user, it was noticed by iPhone causing poor performance. Tap App Store app on iPhone and make sure Facebook App is up to date. If it is then the usual steps with poor battery performance, is to Restore iPhone with iTunes on computer, when prompted at end to Set Up as New iPhone. See if performance is better. If not, make Genius reservation and take to Apple for evalution under Warranty.
Do the Restore, Set Up as New, see if better, if not Apple Store can perform free quick (minutes) battery diagnostic testing. If problem Warranty will cover it. Every battery is different, every user is different but majority of iPhone batteries give great service for most users beyond two years, yours may differ.
I think I am getting closer to the problem...
I just noticed that when I got into my car, the iPhone4S got into a loop to transfer the ContactList to the car through bluetooth:
- transfers the entire ContactList to car
- loses bluetooth connection
- goto step 
It kept on doing this until I'm out of the car and by then, the battery is close to zero.
Looks like either the car is having problem or the bluetooth interface on the phone is getting bad.
Has anyone seen this before?
Well, I solved my problem!!!
Here's how I did it:
- Clean up Contact List: I login to my iCloud account on the web. Looked at every single item in the Contact List and deleted away the spurious characters that were embedded in there by stupid software which converted my MSFT Outlook address book some time ago. Looks like the latest iOS 6.0.1 could be sensitive to these.
- Restore to factory specs: Backed up my iPhone on iTune. Restore the phone to factory specs. And, then Restore that backup onto the phone.
When I went to the car and the phone connected to iDrive via bluetooth. It transferred the Contact List in less than 30 secs and stayed connected over bleutooth. The connection was stable and there were no additional transfers of the Contact List.
Battery is fine now and the phone does not feel hot to touch.
Well, I said it too fast.
The infinite loop regarding the transferring of the ContactList to the car is no longer there.
However, the battery drain issue is still there. I left the house with a fully charged phone and within 3 hours, it was down to 1/2 tank again.
Took it to Apple Store and met with Genius Bar. I set up an appointment online but still had to wait more than 30 mins after check-in.
Anyway Genius Bar ran hardware diagnostics and nothing was wrong. Bluetooth interface was tested using a keyboard and it seems to work fine.
So, he suggested wiping out the whole phone and start from scratch, like it is a new phone. He thinks it was software related.
We'll see if the battery drain issue goes away... also, while the phone was in my pocket, it was starting to burn my thigh because of the heat.
Went back again (the third time) to Genius Bar (GB). After removing WhatsApp app and charged the phone to 100%, the battery power drain tapered off a little but within 3.5 hours the fully charged phone was down to 47% again. No idea what's going on. GB replaced the phone with a re-manufactered phone at the store.
We'll see how this one goes.