It's probably a botnet performing automated SQL injection checks on your site; you definitely need to make sure that you are correctly sanitizing any user input

It's probably a botnet performing automated SQL injection checks on your site; you definitely need to make sure that you are correctly sanitizing any user input, especially if it's echoed back to the page (XSS) or used directly in a database query (SQL injection). Especially if you're having database problems, you're going to want to check things. If you have a database of accounts, you might even consider taking the site offline until you can verify that it is secure (and that it hasn't already been dumped to an attacker).