USB Ports Keep Activating and Deactivating

I have an Apple Thunderbolt Display that I probably got at the end of 2011. Whenever I unplug my MacBook from the display, any USB device that I have plugged into the monitor start activating and deactivating repeatedly, as if cycling power. This happens to my iPhone and to my Pebble watch. I've had this problem for at least a year but I can't say how long. Is this a sign of the display getting old, or is there something I can do to fix it?