A liquid nitrogen-cooled prepolarization ($B_p$) coil made for ultra-low field nuclear magnetic resonance and magnetic resonance imaging (ULF-MR) designed to generate 7 mT/A was fabricated. However, with suspected internal insulation failure, the coil was investigated in order to find out the source of the failure. This paper reports detailed build of the failed $B_p$ coil and a number of analysis methods utilized to figure out the source and the mode of failure. The analysis revealed that pyrolytic graphite sheet linings put on either sides of the coil for better thermal conduction acted as an electrical bridge between inner and outer layers of the coil to short out the coil whenever a moderately high voltage was applied across the coil. A simple model circuit simulation corroborated the analysis and further revealed that the failed insulation acted effectively as a damping resistor of $R_{d,eff}=6{Omega}$ across the coil. This damping resistance produced a 50 ms-long voltage tail after the coil current was ramped down, making the coil not suitable for use in ULF-MR, which requires complete removal of magnetic field from $B_p$ coil within milliseconds.