When you get mail or send it, you will be asked for the password and offer an opportunity to save it. There is no enter password and save it dialog like you are looking for.

Occasionally following the deleting of passwords no prompt appears. This is almost always because the anti virus has a password vault of some sort and is supplying a password from that source when one is requested. In this case there is usually a password error as if you had deleted nothing, or Thunderbird was dragging your old password from somewhere to use.