My iphone 5

make sure you have the latest iTunes version. For today it is 10.7

http://www.apple.com/itunes/download/

Syncing with iTunes on a Mac or PC requires:

Mac: OS X v10.6.8 or later

PC: Windows 7; Windows Vista; or Windows XP Home or Professional with Service Pack 3 or later

iTunes 10.7 or later (free download from www.itunes.com/download)

From Here > http://www.apple.com/iphone/specs.html

If you already have the Latest Version of iTunes...

See Here > http://support.apple.com/kb/HT1808

You may need to try this More than Once..

Put it into recovery mode to get it to appear in iTunes.

To put it in recovery mode:

1. hold down home and power until it goes black

2. release the power button (while still holding the home button) for another 5-10 seconds

3. while holding the home button plug in the USB cable

If done right the phone should be completely blank no more on and off or the itunes screen will be shown and hope itunes recognizes the phone. Then you can do a restore. Hope you've been backing up to iCloud.

Message was edited for clarity.

That happens sometimes, what did the message details say? sometimes best bet is to try again from the beginning.

Some Users have reported that it has taken as many as 7 or 8 attempts using Recovery before success...

Keep trying...

Error 9

This error occurs when the device unexpectedly loses its USB connection with iTunes. This can occur if the device is manually disconnected during the restore process. This issue can be resolved by performing USB troubleshooting, using a different USB dock-connector cable, trying another USB port, restoring on another computer, or by eliminating conflicts from third-party security software.

Sounds to me like this could be connected to the constant reboots, keep trying to put it in restore mode and recover it. You may need to go to an apple store if you can't get it after 10 attempts. Let us know if it starts working.