Based on the syntax you posted, I assume you're trying to consume the GP service in the "arcpy" way?
You're passing user/password via the ImportToolbox arcpy command?
Based on your comments it behaves differently depending on how you publish (secure vs non-secure), and the error - it sounds like your virtual directories might not be right? Which could be an HTTP vs HTTPS issue.
Taking Python out of it, can you make a connection in ArcMap to your secure server (with a USER connection), and consume the service and get back a result. It looks like your result is a Zip file, so you'll have to open the Results window, expand the execution and double click the output to open the Zip.