Yes, in password mode the text will not be sent to client, this is done with security concern. I think the same behaviour has the asp:TextBox as well.
When you have password input in your page, you should expect the user to enter it, and you should not ever send it to the client. Moreover you should not store the password in clear view server side, and need store hash of the password, but that is a long story.
If you do some validation, for example have registration form and the user was not filled something that is required, the next postback does not send him the password, just store this password for you in the session if you like. And on the next postback if the password is empty read it from the session. Or if it is not empty, then the user has changed it, so read it from the input value.
You can set some empty message to the TextBox like and it will looks like it is filled.
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