Again, do a hard reset. You need to upgrade to 5.0.1. This has worked for people on other models of iOS devices.
Please include all information related to your device including the following.
Detailed information about device, Model, etc. (Saw the network log which was good in another post. )
1. Review all your apps and the notifications settings. Check for improvement.
2. Quit running apps by tapping the Home Button in an application. When the APP pop onto up press on them until you see the minus button. Try exiting them one at a time to narrow it down to one particular APP.
3. If you are a developer check your logs, this is the best what to see what is going on.
4. Review your network and push settings.
5. Review who you are getting calendar and messaging from. Google, exchange, etc.
As I have stated we have had no problem, our devices go about 2 days using heavy network traffic.
You should if you are posting here any issues include the following so we get a sense of the what we are really dealing with and it will help.
Device : (Include Ram and APP list if you can) (App list is important.)
Using iCloud:Yes/No
How you are charging: (Direct Plug or using a computer)
Computer including running OS. (Example Mac Book Pro 2009.)
Calendar:(Google/Exchange/iCloud)
Mail:(Again as above.)
Other Network apps: Twitter, Facebook, etc.
Network Carrier:AT&T, Verizon, Sprint, etc.
WIFI usesage: (Percentage for example 20% of the day) and type of network device. Airport 2010 2&5 gig auto switch, older newer, etc. B/G/N
Is the phone or device ever been jailbroken or altered in any way from the original agreement: Yes or No.
Did you have APPLE migrate you data in the APPLE store? Yes or NO
Again, we have lots of the 4s and they are great, the battery is about 2 days. It may be better to get some accurate information to help.
All else fails
Backup and encrypt your iPhone and than reset it to Factory settings. Apply the iOS 5.0.1 update and restore the backup.
This has worked in pass hardware and software updates for us when we experienced performance problems.
Also make sure to update all APP on device.