I may be mistaken, but I don't think you can obtain that. The reason being when accessing PDM through API you are creating a new connection versus latching onto an existing one.
The VaultAdmin tool and SW Explorer tool allow to save the password - but you'd have to find out where it is saving it too and hope it isn't encrypted.
Probably better to work with your VAR to reset the password if you cannot login. But otherwise yes, Matt is right using the API creates a new connection.