I appreciate the help. I looked into my PayPal account, and I don't have a security key enabled, so that's not the problem for me.
Yes, I do have my merchant id configured with s2member. Though after looking at what Christian shared, I realized that my unsubscribe button is still using my merchant email address in the URL it generates instead of my merchant id (maybe I need to regenerate the short code?). So as an experiment, I replaced:
https://www.paypal.com/cgi-bin/webscr?cmd=_subscr-find&alias=my email]
With
https://www.paypal.com/cgi-bin/webscr?cmd=_subscr-find&alias=my merchant id]
On the up side, I now get this message when I'm redirected to PayPal:
"To cancel a specific subscription click on its details. This will take you to its details page where you will find a Cancel button."
On the down side, no subscriptions are listed! Under "All Activity" (within the correct date range), there's nothing there. So this actually makes the situation worse, because with the previous error message, it at least provided a link to where users could find their subscriptions and cancel them.