How to debug “spam” problems?

I am one the (apparently) hundreds of people who have encountered the problem in which suddenly all attempts to post email results in the dreaded “There was an error trying to send your message. Please try again later.” error message, enclosed in an orange (“spam”) box.

I have read the FAQ, along with many, many similar posts about this problem, but no useful information is presented.

How can we debug exactly what is causing Contact Form 7 to think there is a spam situation? Is there any way the plugin can output error/debug info to one of the log files. (I have WP_DEBUG enabled, etc.)

My setup:
WP 4.6.1
Contact Form 7 4.5.1
Postman SMTP 1.7.2

Unfortunately, this site is behind a firewall, so I can’t expose it. Again, email posting worked great for the first few days in which I had everything configured, but then today it suddenly stopped working. Between the time it was working fine and today, no additional plugins were installed or removed, and no significant configuration changes were made.

Please note that I am not asking you to fix my problem, but rather assist ALL of us in helping us to help ourselves by pointing out any and all ways we can debug the process.

Thanks in advance.