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next time it happens, log into phpMyAdmin or the equivalent on your site and take a look at your SQL database. The error messages you receive on your blank homepage look like the ones i get when my site exceeds the max_questions resource for SQL queries.
If it is the same issue for you, the issue should be periodic, especially when you are installing modules or during heavy traffic on the site, like in chat or forums, and the site should miraculously re-appear usually within one hour.
When you log into your SQL dbase, instead of seeing the database structure, you will see an error message indicating max_questions exceeded. (that is, if it is the same issue, which it may be).