Signal losses after restoring. Why?

Hello,

I currently have a problem with my iPhone5c’s signal, bought from September last year. It suddenly started a few days ago.

My signal on the phone keeps on failing. It keeps on saying “Searching…” and it sometimes catches the signal and would say “EE 4G”. However, instantly afterwards, it switches back to “Searching”. This repetition happens continuously and not only unable to connect 3G, but I cannot even make a call or a text to people.

Also, when I try to go to “Settings” and to “Mobile”, it refuses to open and goes back to the main page.

When I erase all the content of my iPhone and start it up as a new phone, the problem seems to get sorted. The phone will get its signal back. Nevertheless, when I try to restore the data from iTunes to the phone, the problem also comes back. No matter how many times I tried, the result seemed to be the same. (I have tried it 4 or 5 times). From this, I believe the problem is not on the iPhone’s hardware, but in the software.

I have taken my phone to the Apple Geniuses counter, but they told me the problem should be on the software and if restoring brings the problem back, it is best to set up the phone as a new phone as finding one part that is causing a problem will be difficult. I have tried it myself, but the problem remained the same even when I deleted all the apps and the photos and refreshed it. I have even updated all the apps and the iPhone’s software into IOS7.1, but it did not help.

Does anyone have any idea of fixing the problem without losing all the photos, apps, music data that currently sits on the phone?

As I am out of ideas I would appreciate for any ideas or tips.

Thank you for reading such a long statement.