I was being hammered by more than a hundred hack attacks each night, so I hunted around for a security plugin that would put an end to their efforts. I installed Better WP Security, and the problems vanished!
Make sure you back up everything before you start though. I'm not the sharpest pencil in the box when it comes to making changes to the WordPress backend - and I managed to lock myself out a few times before I finally understood how the bits and pieces of the plugin work. I had to reload from backups a couple of times - but in the end, the effort was worth it.