Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
How to Back Up Your Device With iTunes
Whether you own an iPhone, iPad or iPod, chances are you have some very valuable things stored on their. It could be certain apps, your music library or more important things such as documents and contact details. Whatever you have on there, the last thing you want to do is lose it all which is why you should always make sure you have everything backed up and ready to restore if you need it. This is easy to do and takes only 5 minutes of your time so there really is no excuse. Back up is free and Apple customers have two easy options: iCloud or iTunes.
This is how you do it through iTunes:
One of the benefits of using iTunes is that you are not limited in the same way as with iCloud, which allows 5GB before you have to pay. With iTunes, the only limit is the space you have free on your computer, although it may be wise to back up everything in a second location too in case anything happens to your Mac or PC.
Before you proceed, you should check that your iTunes is updated as the latest version would be ideal, if not necessary, for this.
There are two simple ways to back up with iTunes:
First off all you need to turn iCloud off by opening your Settings, then selecting iCloud. You can toggle iCloud on or off with Storage & Backup.
Next go to Settings again only this time choose General and go to iTunes Wi-Fi Sync. When you are presented with a list, click on your computer.
There is a Sync Now option although you shouldn’t have to click this. If the screen of your device is locked, the device’s Wi-Fi is on and it is connected to a power source, it should sync automatically.
Once again, you will need to disable iCloud as outlined above.
Connect your device to your computer with the appropriate cable and open iTunes.
In iTunes, look under Devices for the one you are backing up and right-click on it. Select Back Up.
Of course backing up is only half of the battle. Hopefully you will never be in a situation to need to restore your device but if it does come up, here is how it is done:
Connect your device to the computer.
Once again turn your attention to Devices and select the one that needs restoring with a right-click.
Choose the Restore from Back Up option if you can see it, otherwise you need to click on Summary and then select Restore.
You should then see the message “Restore in Progress” on the screen of the device, while a progress bar in iTunes will show you how far along the process is.
When restoring is complete your device will restart. Before you disconnect the device however you will need to wait until the progress bar has finished and the device is completely rebooted.