Why are you ejecting the drive? If it's a drive you use for backups or consistently, it's far better to keep it plugged in. This way you can take advantage of spotlight indexing the drive on the fly as opposed to doing it every time you plug it in.
When you eject a drive, OS X assumes you are going to be powering off or disconnecting the drive. So, in doing so, it removes the drive from the list of available drives. When you power on the drive again, and it is plugged into the computer, OS X automatically mounts it.
So...what exactly are you asking?