If the problem persists, you may have to use a true sine wave inverter. As long as you don't mount in the engine compartment or outside the passenger compartment. Engine compartment temperatures are too high and will damage the unit. Mounting the device outside the passenger compartment can subject the unit to high heat, high humidity or direct moisture which can also damage the unit. That depends on the battery capacity and the current drain.
Inverters run hotter as the load increases.
It is a good idea to make sure that the inverter gets plenty of air circulation. Inverters that produce a modified sine wave have a tendency to fool most Volt-Ohm meters. Very expensive Volt-Ohm meters account for varying wave shapes and will show the output at 115 Volts AC nominal.