Not likely. More likely it's the wiring between the inverter and the battery. Prove it by connecting to battery negative, then to inverter output negative. If the lights go bright, it's the negative connection. If nothing happens, connect to battery positive and inverter positive. If the lights go bright, it's the positive connection.
In my case the negative wire on the inverter negative that connects to the battery was so loose it was just dangling in the socket. Plugged in, it took 3 days to drain the batteries. Running the engine feeds the battery on different lines.
Use your meter to check inverter output on the inverter output terminals before blaming it.