@Jason Hendriks
The person reporting the problem is saying that it's not an authentication (password) issue. Where are you getting that information from? She's saying the problem is still occurring so I was offering my assistance.
@Sarahlevinger
I'm only sharing my experience because I'm also using Contact Form 7 on Wordpress with GoDaddy and was having the exact same problem (granted I'm using Google Apps for email). No authentication required and I have an SPF record for Google and SecureServer and the form works perfectly.