[AnotherCat]

I would have assumed that the Kobo is an MTP device (I don't have one so don't know)? If so there is no concept of "eject" as there is for a USB mass storage device and due to the "transaction" nature of MTP and its having no need for the computer to have exclusive access to storage means that ordinarily there is no need to connect or disconnect anything for data protection, the device can just be left connected. That would seem to cover needs of the type alluded to, in which case I wonder what the OP's special need is?

But if the Kobo is a USB mass storage device then as far as I am aware if a user ejects a mass storage device there is no means to reconnect it in Windows itself (and relying on the other posters, nor from Calibre either), however there are third party USB device management applications for Windows which claim to do so and a Google search should turn them up.

Another but. I know Calibre has an "Eject this device" menu option even when a MTP device is connected so it may have some selfish need of its own for the user to rid it of the presence of the MTP device. If so, then I think one is likely out of luck if one wants to reestablish data transfer between the computer and the device by software after doing so, unless that ability were to be built into Calibre itself. But I am happy to be schooled on that, I know nothing about Calibre's innards and selfish needs.