It happens to me quite often that the left mouse click in Hyper-V is no longer registered in the ‘Virtual Machine Connection’ app.
I previously solved this by shutting down the virtual machine, and closing any Hyper-V apps. Googling around for some time, I found a better solution – Save the Hyper-V machine state, and once saved, start it again. It will fix the mouse button issue.
Saving might sometimes be a problem, especially if you use Virtual Machine Connection for the same purpose as I do – namely to use virtual machines to connect over a VPN that closes external connections. Try doing this over remote desktop and you notice you lose connection to the virtual machine for good. But in my case, the Save -> Start operation is quick enough for the VPN connection not to break, but to simply reconnect after this 5 .. 10 second operation.