How do I prevent the MAX4080 from giving a false output reading?

The MAX4080 is a current-sense amplifier capable of sensing currents with a common-mode input voltage range up to 76V.  In order to perform according to the datasheet specifications, both the VCC voltage and the common-mode voltage applied to the RS+/RS- pins must be above +4.5V.  If VCC is applied and the RS+/RS- pin voltages drop below +4.5V, to 0V in common cases, the output of the MAX4080 may be a non-zero voltage.