In addition to that document, I see in our notes that one user reached out to WordPress and found out that their ProfilePress plugin was automatically updated, and this caused the Zap to no longer be able to connect. Downgrading back to the previous version (4.3.1) fixed the connection.
Another ended up reaching out to their site hosting provider, Cloudways, who resolved as follows:
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.