This started as a support request, but I figured out the problem, so thought I would report what happened.
I've been using admintools for maybe three months, including the WAF to block attempts to access the admin section of our site. Last I looked a week or so ago, there were about 1200 entries. We receive emails every few minutes with more unauthorized attempts being blocked.
I started looking through the admintools tables, and noticed several were quite large. _admintools_ipautobanhistory had 8000 entries and _admintools_log had nearly 350,000 entries. This is apparently what caused the gateway timeout error.
Deleting the contents of the log fixed it. I also deleted the ipautobanhistory entries.
Given we've changed our /administrator/index.php to use the "Administrator secret URL parameter", is it really necessary to also use "IP blocking of repeat offenders" and the "request filtering" options?
What are the performance implications of using these additional blocking methods?