I found that the common configuration available on the Internet didn't work for me. Specifically, the Apache Rewrite rule needs to reference DOCUMENT_ROOT. Here are my rewrite rules; remember that for this to work, they have to be first:
I am a computer programmer and racounteur entrepreneur based in Baltimore.
RewriteCond %{DOCUMENT_ROOT}system/maintenance.html -f
RewriteCond %{SCRIPT_FILENAME} !maintenance.html
RewriteRule ^.*$ %{DOCUMENT_ROOT}system/maintenance.html [L]