Issues with drivers installation and board connection to / disconnection from pc

I've installed the complete package (Arduino software and drivers) on a PC running Windows 7. The installation seems to be successful as in the list of the installed modules I can see only green check signs. Unfortunately, when I connect my Genuino Uno, Windows starts searching the drivers online; if I cancel the search, the board is not recognized, it appears as "unknown device" in Device Manager and I cannot upload my sketches from the IDE; if I wait for the search to complete, everything works fine.
If I disconnect the board and connect a new one to the same USB port, the process starts again: the board is not recognized unless I wait for Windows to download and install the drivers from the Internet. The problem is: this online search takes a lot (more than 3-4 minutes) and I need to connect/disconnect the boards very quickly to test the projects of all my students.
What's going wrong? I've installed the IDE and drivers on many computers before and everything's been working fine. Why, once the drivers seem properly installed, disconnecting the board and connecting a new one requires a new installation?