I did some digging into our notes, and it appears that the problem may be caused by CloudFlare. The user reached out to their site hosting provider Cloudways who resolved as follows:
For another user, in Cloudflare, “Firewall > Bots > Configure Super Bot Fight Mode > Definitely automated” was set to Challenge, preventing the Zapier connection from succeeding. Changing this to “Allow” allowed the Zapier connection to succeed most of the time, but not all of the time. In Zapier there are two versions of the WordPress "app". The “non” legacy version of the WordPress app in Zapier seems less stable. The “WordPress (Legacy)” version connects more consistently.
In Cloudways, enabling “XMLRPC Access” in "Application Settings > General" allowed the Zapier connection to succeed 100% of the time.
In addition, one of our awesome Community members ran into a similar error and was able to find a solution on this post:
I'm sorry to hear the Jetpack Protect settings change did not resolve this issue for you. Could you please try these troubleshooting steps on this help article and let me know if this works for you?