Thanks Ken,
To answer your question, the domains of the users' e-mail addresses are quite varied (Gmail, Yahoo, international addresses, etc.).
I appreciate your help with this very much, but fortunately, the issue now seems to be resolved. After running a number of tests, I noticed that the e-mail notifications would go through (although not immediately) after I would manually run the cron script (by going to mysticalmindtraining.com/admin/crop.php). I had a feeling that the root of the issue was related to cron and, after making a small setting change on the server, everything seems to be working correctly now.
The change I made was under the "Scheduled Tasks" section (Parallels Plesk 11.0.9) for the domain, where I had configured cron to run every half hour. On a side note, the command that seems to work best for me is "wget -q -O /dev/null http://www.mysticalmindtraining.org/admin/cron.php" but the setting change that I made to resolve the issue was actually in the "Minute" field. I used to have "0,30" and I changed it to */30 (and then again to */15). After making that change, everything has been working as would normally be expected (i.e. all notifications are going through and are received usually within 15 minutes).
If anyone has any thoughts or comments about this, I'd be interested to hear them, but otherwise, I feel this issue is resolved. Thanks again Ken and I'd also like to send a big thank you to you, Matteo, for helping me through the troubleshooting process. That was invaluable!
Blessings,
Jason