Depending on the computer system and the type of USB webcams involved, the computer's USB bus can have trouble activating more than a couple of webcams at any one time.
One thing you can try is to choose "No Audio" for each camera entry to see if that has any effect. (The idea being that if the microphone portions of the webcams are not enabled then there may be enough power available for the three video streams.) This may or may not work, again, depending on your specific system and cameras.