From what I"ve read elsewhere, these symptoms could be caused by low voltage on the Pi board, causing it to drop out when a higher-power device draws current from the RasPi USB host port, and/or the ethernet chip is trying to drive the cable, and/or the CPU in the SoC draws more current.
This could be caused by (for instance): low current/low voltage from power supply, high resistance USB cable, bad connection on microUSB connector, out-of-tolerance polyfuse on RasPi board, and probably other things. I don"t know what is the most likely.
If you use a voltmeter or multimeter to measure the voltage between the "5V" (P1-02) and "0V" (P1-06) GPIO pins, you could confirm a low voltage issue if it measures anything lower than 4.75 V.
For the map of the GPIO pins, see http://elinux.org/Rpi_Low-leve.....eripherals
How to use a voltmeter: