Right now the SSH setup in ST4Win means that only key-based authentication is supported. This is because plink ignores the SSH_ASKPASS environment variable and doesn't call askpass. When you use a HTTPS URL, it's actually Git that calls the SSH_ASKPASS hook so manual authentication works.

Might need to fork plink to support this, or alternatively use TortoisePlink which provides its own version (although in that case saved passwords wouldn't be supported in the same way so that would be less effective)