Site unreachable by WPMU plugins while using Cloudflare Flexible SSL

The website is reachable but I am seeing an error message with WPMU's uptime and blacklist monitors which read "Your domain does not appear to be publicly accessible on the Internet. We can only monitor the uptime/blacklist status of public websites." I have a suspicion that the problem is that my site sits behind Cloudflare's Flexible SSL and all http traffic is redirected to https. I would really like WPMU plugins to work in this setup. Is there something I can do to resolve this error without changing my network configuration?