Aren't those active low? Don't you feed 0V to turn on and 5V to turn off?
Can be a problem because USB can't supply much power. And even though it's triggered through a opto and a transistor, the power has to come from somewhere. Although, I think most USB should be able to drive a single relay.But I think it's a god time to start reverse engineer the board a bit. I would start by checking where Vcc and COM are connected.
COM-D1 1062[Ohm]COM-D2 1016[Ohm]