We can take a look at this directly for you if you'd like to contact support, but how long is it taking for the message that do arrive to arrive or has it been over 30 minutes?
Are you using aol, gmail, hotmail, msn, or yahoo email addresses for testing? Those won't work in the From value on forms on our hosting.
Here's more info here: http://support.godaddy.com/godaddy/having-problems-with-your-websites-form-mailer/
If you would like us to look at what's up, send us a ticket at http://x.co/heretohelp and respond to this with the ticket number and we'll take a look for you.
^Cj