Just as an update, I now see this is happening on ALL of my subdomains, not just the ones with custom domains. So, it doesn't seem to be your plugin.
I think it might be from BPS, but I'm not sure. I've tried talking to my hosting provider, which is GoDaddy (I know, I know), but they seem to not have a clue about multisite.
Anyways, I just wanted to let you know what I found out and to say thanks for all of your help.
Obviously, I don't expect you to continue troubleshooting this for me, but if you have any suggestions as to a direction in which I could go, I would be most appreciative.
Thanks again! :)