Just have that page send out anti-caching headers every time a user loads it. This will force the browser to get a fresh copy of the page every time. You can do this without affecting the caching of the other pages in the site.
You can use meta tags:
<META HTTP-EQUIV="CACHE-CONTROL" CONTENT="NO-CACHE">
<META HTTP-EQUIV="PRAGMA" CONTENT="NO-CACHE">
<META HTTP-EQUIV="Expires" CONTENT="-1">
In PHP send http headers (You'll have to tell Apache parse the file as PHP)
Header( "Last-Modified: " . gmdate( "D, j M Y H:i:s" ) . " GMT" );
Header( "Expires: Sat, 26 Jul 1997 05:00:00 GMT" );
Header( "Cache-Control: no-store, no-cache, must-revalidate" );
Header( "Cache-Control: post-check=0, pre-check=0", FALSE );
Header( "Pragma: no-cache" );
In Apache .htaccess
<FilesMatch "index.html$">
FileETag None
<IfModule mod_headers.c>
Header unset ETag
Header set Cache-Control "max-age=0, no-cache, no-store, must-revalidate"
Header set Pragma "no-cache"
Header set Expires "Sat, 26 Jul 1997 05:00:00 GMT"
</IfModule>
</FilesMatch>