Mosquito-borne flaviviruses are significant contributors to the arboviral disease burdens both in Australia and globally. While routine arbovirus surveillance remains a vital exercise to identify known flaviviruses in mosquito populations, novel or divergent and emerging species can be missed by these traditional methods. The MAVRIC (monoclonal antibodies to viral RNA intermediates in cells) system is an ELISA-based method for broad-spectrum isolation of positive-sense and double-stranded RNA (dsRNA) viruses based on detection of dsRNA in infected cells. While the MAVRIC ELISA has successfully been used to detect known and novel flaviviruses in Australian mosquitoes, we previously reported that dsRNA could not be detected in dengue virus-infected cells using this method. In this study we identified additional flaviviruses which evade detection of dsRNA by the MAVRIC ELISA. Utilising chimeric flaviviruses we demonstrated that this outcome may be dictated by the non-structural proteins and/or untranslated regions of the flaviviral genome. In addition, we report a modified fixation method that enables improved detection of flavivirus dsRNA and inactivation of non-enveloped viruses from mosquito populations using the MAVRIC system. This study demonstrates the utility of anti-dsRNA monoclonal antibodies for identifying viral replication in insect and vertebrate cell systems and highlights a unique characteristic of flavivirus replication.