Tony,
I honestly don't know. JFBConnect only sends emails when a new user registers on your site. If you're seeing "Could not instantiate mail function. " message, it means there's some extension trying to send an email when you're navigating. That could be plenty of things, like a backup finishing and sending an email to the admin, a notification to a user about a new private message (from JomSocial, for example), or about a thousand other things.
The main thing to determine is why the mail function can't be instantiated. I honestly don't think things have to do with JFBConnect, but we'll gladly help how we can. I'd recommend doing the following:
1) Check that other emails are being sent. For example, new user registration emails, admin notification emails (for new users) or anything else that you know triggers an email.
2) Check your settings in the Joomla Global Configuration area for mail. Try different options, like PHP Mail or Sendmail to see if those improve things or hide that message.
Let me know how that goes. Basically, from here, you just need to narrow down a) what is trying to send an email and/or b) why the email sub-system isn't working (either sometimes or always).
I hope that helps get you started,
Alex