I concur with sleeplessinDC. 404s are being generated on /wp-admin/admin-ajax.php, referred by wp-admin/plugins.php, whether:
1) I insert an .htaccess file inside the wp-admin directory that allows access to the wp-admin directory only from my IP address; or
2) I password-protect the wp-admin directory.
Plus, when applying password protection on the wp-admin directory, I cannot login myself via WP's login screen.
Is it possible to protect the wp-admin directory without blocking my own login? (I'm the only user on my site.) Plus, are the 404s referred to above nomal? I only ask, because I use a plugin that notifies me by email whenever 404s occur, and they're coming in fairly frequently.