Carbon nanotube (CNT) conductive composites have attracted significant attention for their potential use in applications such as electrostatic dissipation and/or electromagnetic interference shielding. The focus of this work is to evaluate resistivity trends of extremely low loading (<0.1 wt%) epoxy-CNT composites that lack a connected CNT network, but still present electrical conductivity values appropriate for those uses. The impact of current, temperature, and cycle life on electrical properties are here identified and tied to possible performance limits. At extremely low loadings, the CNT content is not sufficient to form a completely interconnected grid, thus, electrons must travel through insulating media. While still in the semi-conductor range, resistivity values are observed to decrease with increasing direct current and demonstrate a non-ohmic behavior. CNT epoxy composites were subjected to elevated currents and/or temperatures over diverse periods of time to examine impacts on resistivity. Microstructural analyses of composite samples were conducted to observe signs of damage for specimens taken to extreme temperatures/currents. An understanding of the electrical conductivity characteristics of extremely low loading epoxy-CNT composites and their failure mechanisms will aid in understanding risks associated with their use in challenging environments that may include high temperatures, high currents, and/or high frequencies.