what is the problem with the drive? Hardware issues normally cannot be cured with firmware updates.
Also, notebook drives are customized for the notebook manufacturer, so a HP notebook (just an example) and an Asus one seem to have the same drives (according to the name), but they are slightly different and have different firmwares. You can't flash your Asus version into a HP version. For newer firmware, you have to check with the manufacturer of your notebook.