Zoiper works fine with sipgate, we have a lot of users using that provider.
I don't know why you are getting 401, it sounds like wrong username or password. Please check with them if they can see the exact reason. (they reply 401 to us, that is all we know :/
Are you having the problem on registation or only when trying to make a call ?
If its the latter, the issue might be with the codec or with the prefix