iPhone 4 keeps going out of DFU mode when trying to reset

So I was helping my dad with his iPhone 4. It just stopped working from time to time.
When I tried turning it back on at those times, it just stops at the recovery mode screen. I then tried having it plugged in while I had iTunes up, but that didn't help. Error 21, iTunes said.

So I tried putting the phone in DFU mode and then resetting it to factory settings. But during the reset - when it tried to contact the Apple servers - the phone went straight from DFU mode to Recovery mode which gave me the error 21 again.

I've tried all of the tips in the help section (making sure that the computer was up-to-date, I made sure the security program was turned off etc, I deleted the ipw and had iTunes download it for me again), but that didn't help either. I even tried to start iTunes as an administrator, but that didn't help either. The account on the computer is also an administrator.

So what should I do now?