Any USB device should get re-polled by simply unplugging, and then plugging back in to a USB port. That's how you get it to work....
I was really asking you to clarify how you connect your other USB devices, as a flaky external USB hub can cause a variety of problems, especially one that's bus-powered.
You didn't say, so I'm guessing that you need to swap devices at some point, and that's why you disconnect the keyboard?
Is it always the same other device? And do you have any problems with THAT device?
If your mini does not see the keyboard when you plug it back in, then I suspect the USB chip in the keyboard, so try a different keyboard for a few days, to see if the problem goes away. I suspect it will, unless your problem is a result of the connection by that other device.
I have a couple of different non-Apple keyboards - a Logitech that I really like, for example. The problem is not being an Apple part, or not - but that the USB chips in those devices sometimes start mis-behaving. Your best test is a different keyboard.
I see I didn't really answer your question about a command of some kind to reset the USB bus.
I don't know the answer, although someone else might chime in on that. I rely on the USB bus just working (seeing the device when you plug it in, and simply working. I expect the same on a Windows PC, for example, assuming the driver is already installed and available for the device that you want to use)