There are lots of questions that ask about the 80072ee2 "The operation timed out" error in msxml3.dll, but most are resolved by moving the requested URL to a different application pool. But, we already do this and are still getting this error on a semi-regular basis.
We're running a Windows 2008 server and IIS7.5 - the website is Classic ASP and the code is:
set xmlhttp = CreateObject("MSXML2.ServerXMLHTTP")
xmlhttp.open "GET", "http://www.mysite.co.uk/_search/search.php", false
strResponseText = xmlhttp.responseText
set xmlhttp = nothing
Your code looks absolutely fine. Two things you can try though.
This may not make any difference, but you're msxml6.dll - which is present on IIS7 - rather than the older msxml3.dll
Second, if you have Remote desktop access, see what happens when you try to access http://www.mysite.co.uk/_search/search.php from the server's own copy of IE. I've encountered situations where you can't see a site the server hosts itself through the external URL and you have to use localhost or 127.0.0.1