I believe I have discovered the problem - the Dell XPS 13 Touch (model 9350) has 2 USB 3.0 ports. The USB port on the right side is a "PowerShare" port according to Dell. When I have the Targus dock plugged into that USB port I experience the issue, however I've had the USB cable plugged into the port on the left side of the laptop (a non-PowerShare port) for 2 days and have not had any problems.

Today I plugged the USB into the right side PowerShare port and the problem occurred twice within 10 minutes. Looks like PowerShare is causing an issue.