Just wanted to share the official verdict for the difficulties we have been having with the site.  The following comes from the company that hosts us....

 "The source of the problem was a security leak in the cPanel software. Its developers managed to locate it and released a security patch. We have immediately upgraded the cPanel on all our servers, two weeks ago, and this way the problem was permanently fixed.

Unfortunately even though very rare, these kind of malicious attacks happen, the hackers did not target specifically our company or your website. This virus was a large problem for all web hosting companies. Thank you for your patience and understanding."

 So there you have it!