This happens to me too with my daughter's iPhone 3GS on iOS 6.1.4 and the latest version of the Configuration utility for Windows (3.6.2.300). I think it has something to do with certificates and signing. It's possible that the iOS 6.1.4 is too new for the iPhone Configuration Utility. It seems like the new way to do this is with the new Apple Configurator, which only runs on Macs. :-(
However, as a workaround, in the iPhone Configuration Utility for Windows I clicked on the configuration profile I wanted to install, clicked on Share, changed security to None, and clicked Share. This opened up an email with the configuration as an attachment. I sent the email to the phone. I then opened that email on the phone and installed the profile by tapping on the attachment. That worked fine as long as the profile was not signed. (I think the certificates for signing may be out of date or something like that?)