Q: why isn't my phone backing up?

Since you posted this in the iCloud forum, I'm guessing that you are referring to an iCloud backup. Is your device connected to power? Do you have a stable Wi-Fi connection? Is this the first time that you have backed up the device? Do you have sufficient room in iCloud for the backup?

The length of time then would be dependent on the amount of data to backup and the speed of your internet connection. How much space did iCloud estimate for the size of the backup?

I have the same issue currently, just with the open beta of iOS 9.

Do you have the issue with iOS 8 or 9 ?

You can try a reset by holding the sleep/wake and home buttons together until you see the Apple logo and then release. The phone will reboot. This will not have any affect on your data. You can also check out the troubleshooting in this support document about iCloud backups. Get help backing up your device in iCloud - Apple Support

Update: now it´s working again, it just finished.

You cannot have just updated your device to iOS 8.1. That is no longer being signed and cannot be used. Is your device jailbroken or otherwise hacked in any way? What version of the iPhone are you using?

You do not have the choice which iOS you update to. If you connected to iTunes and attempted an update and it wouldn't, then you must have already been on iOS 8.1, since you cannot update to that. How much free space do you have left on the device that you couldn't update? Sounds like you have too much content on the device, and that could be why you are experiencing problems with the backup. I would go back to the support document that I provided the link to.