Hmmm, that sounds odd. I've been using this for years in multiple domain environments with no trouble. Additionally, it's just a straight ADO connection using integrated security, so as long as you have admin rights on the remote machine, it shouldn't be a problem. How are you launching it? You should be saving the .hta file to your local machine and then just doubleclick on it to launch it. Is that what you're doing?
If you're able to connect to the database server with SQL Mgmt Studio, then I can see no reason why you shouldn't be able to connect using this HTA. You might want to try running the hta locally on the actual SQL server to see if you can get it to work like that before you try to run it remotely, but like I said, I've used this in many different environments without any trouble. I'd be curious to hear the specifics of your environment and how you're trying to run it. Might want to look at the authentication for the SQL server in the SQL Configuration Manager on that machine.