Reupload all your core files, except for config.php. Then see if it you still run into the same problem. At least then you've eliminated a possibility. Make sure you upload an unedited batch.
As I said, it doesn't necessarily matter if you have edited any of them or not. Errors can still happen. Did you do as suggested? We can't help unless you let us know.
You say this problem happens on all four sites on the server... did this problem just start or has it been happening ever since you started using this server? Have you checked your error_logs?