BPS does not block you from editing your wp-config.php file. The only thing that BPS does regarding the wp-config.php file is BPS protects it from being accessed directly via a Browser/HTTP (not FTP).
What you should check is this:
Have you locked your wp-config.php file with file permissions other than 644 file permissions. If so, then change the file permissions back to 644 to be able to edit your wp-config.php file.
Also are you changing your MySQL password in phpMyAdmin in your Host Control panel before changing your password in your wp-config.php file? You MUST do both things. phpMyAdmin allows you to access and edit your WordPress database to change your WordPress database password.