Talk to your host. I've seen this problem many times, but it often happens when an error log gets so fat it takes up too much space. This is actually pretty common on shared hosting. The issue may not even be your site, it might be another site on shared hosting (if that is what you are using).
When you see an error like this, it is always a good idea to involve your host's tech support on the fix. In the past when I've had it, they needed to go into the server and do nothing more exciting than clear a cache out.
I know how said that the company lacks tech support, but I don't really see anyway around it unless you have full access to the server itself (since the issue might not be you to begin with).
