Loosing the master password (or key or whatever) that is used to generate the passwords for a deterministic password generator is fairly similar to loosing the

Loosing the master password (or key or whatever) that is used to generate the passwords for a deterministic password generator is fairly similar to loosing the password database. One is really not that much more secure than the other particularly when dealing with online websites. But yeah if the site gets hacked you have to pick and remember an iterated password (ie a next iteration) or regenerate a new master password. Of course if you are really paranoid you can always generate a password with dice and write that password down somewhere in safe place (ie offline password generation).