Restart everything including the router and try again maybe even try a PRAM and SMC reset on the Mac. Like mentioned above I would occasionally have this problem as well but that would fix it. It seems to be fine since Sierra for me but I don't use it too often.
AirDrop uses bluetooth to setup what is essentially a wifi direct connection for transfer so both will need to be on. If I wasnt in the middle of a large network transfer I would try disconnecting my Mac from the router to see if it still works. Since it uses wifi direct you shouldn't even need to be connected to a network, this is how it can work when you are aren't on a wifi network on iOS devices but wifi will still need to be on.