Parece que está relacionado ao plugin Wassup. Eu habilito os logs lentos do PHP e recebo o erro abaixo depois que o site falhou novamente, mas durante o dia. Depois que eu desativei o plug-in, o site ficou instantaneamente mais rápido e não tive lentidão nem travou como antes.
[25-Jan-2012 15:09:20] [pool www] pid 3593
script_filename = /home/fez/www/index.php
[0x00007f353cb75890] mysql_query() /home/fez/www/wp-includes/wp-db.php:1091
[0x00007f353cb75670] query() /home/fez/www/wp-includes/wp-db.php:1375
[0x00007f353cb753d8] get_results() /home/fez/www/wp-content/plugins/wassup/lib/wassup.class.php:553
[0x00007f353cb75278] getMySQLsetting() /home/fez/www/wp-content/plugins/wassup/lib/wassup.class.php:180
[0x00007f353cb750c0] defaultSettings() /home/fez/www/wp-content/plugins/wassup/lib/wassup.class.php:232
[0x00007f353cb74fc0] getSettings() /home/fez/www/wp-content/plugins/wassup/lib/wassup.class.php:212
[0x00007f353cb74ef8] loadSettings() /home/fez/www/wp-content/plugins/wassup/lib/wassup.class.php:90
[0x00007f353cb74b10] wassupoptions() /home/fez/www/wp-content/plugins/wassup/wassup.php:1822
[0x00007f353cb749d0] wassupPrepend() /home/fez/www/wp-content/plugins/wassup/wassup.php:326
[0x00007fff788d6280] wassup_init() unknown:0
[0x00007f353cb747a8] call_user_func_array() /home/fez/www/wp-includes/plugin.php:405
[0x00007f353cb74410] do_action() /home/fez/www/wp-settings.php:304
[0x00007f353cb74320] +++ dump failed