IPhone 4s won't update to 6.1.3?

My phone isn't jailbroken. On itunes when I try it says "iPhone could not be updated. This device isn't eligible for the requested build."
I'm on a mac. My itunes is up to date as well. I have tried to restore it but the same error message comes up.

Added (1). I have 4GB of storage left

My iPhone 3GS is ios 6.1.3 but I Jailbroken it, so i don't know about your 4s never had one all though my sister has a iphone 4 that can't update either

You probably don't have the storage!

This is actually the document about updating iOS

http://support.apple.com/.../kb/HT4623

Try doing it through the phone without connecting it to iTunes every time I've updated my software I've done it through the phone itself and it's worked flawlessly.
1) Go to Settings
2) Go to General
3) Go to Software Update
4) Let it search for the update and click on the install option
5) Make sure your iPhone is plugged into the AC adapter so it won't lose power while installing the update or the update will be terminated

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