I have problems when I attempt to upgrade my iPhone from iOS6 to iOS7. I went so many time to general and software update but it will run checking for hours and nothing and I need to have iOS 7 or up.
You can check apple signing status and download the correct firmware and software from ipsw rocks if you need any help then contact me via this site.
Apple has stopped signing iOS 7 for all except legacy products [essentially iPhone 4]
If your device is capable, your only choice now is to go to iOS 8, unless you wanted to risk jailbreaking it.
[Source IPSW Downloads]
That link is also good for downloading the specific ipsw file for that device, allowing you to manually initiate the update from iTunes - covered by How can I restore my device with simply ipsw file and iTunes?