If your default vhost is a heavy dynamic website that is even using mod_rewrite then the fix is easy.
Create a new vhost, example: default.com.
Add a nice plain index.html file to the /var/www/default.com/web folder so that the vhost is as light as possible.
The trick is to make this vhost the default one.
From SSH type:
mv /etc/httpd/conf/sites-enabled/100-default.com.vhost /etc/httpd/conf/sites-enabled/000-default.com.vhost
Now the connections to the Apache childrens are being kept alive using the default vhost.