I'm not convinced that the module itself is not to blame. As I said, it's very old.
If iTransact is telling you it's not them, then I suppose you could look up the error text in the module files and see what sort of error condition is triggering that message to be displayed. Then sort out with itransact why that error condition would be triggered. Basically troubleshoot by reverse-engineering the logic to find out what it's doing or not doing. The itransact documentation should in theory be of some help.

While I can't say with certainty, I'd be surprised if it were a hosting issue unless it's just that the host is blocking the communications to the itransact gateway due to firewall settings.