This is also happening for me: while users get their copy of the message, the message is not received by the recipient.
My work around is to configure the form to use two recipient email accounts. The form data is emailed. However, though the form data is emailed, it’s only received by one of my email accounts (self hosted email), but not the other (a gmail account). Hmmmm.
Also to make this plugin really shine, the user email probably needs a different subject line than the one the admin would use (which in my case has email triggers for rules which look pretty unpleasant to the end user).
Otherwise, this is a terrific plugin. Many thanks!