Thanks for your help. I have isolated the problem to the settings for the SMTP Host. I have SMTP Host set to localhost. My host is Verio. (When I tested using GoDaddy as host, everything worked as expected.)
Has anyone used Contact Form-7 with SMTP Host? Do I need to specify the server path instead of localhost?
Communicating with Verio Support has been a challenging(to put it nicely) so any help would be appreciated.