starter turns the engine over and the engine engages for 1 to 2 seconds and then dies

When starting, the starter turns the engine over and the engine engages for 1 to 2 seconds and then dies. We had the battery replaced and started fine - for about two weeks. Then the car would do the same thing - starter turns the engine over and the engine engages for 1 to 2 seconds and then dies. We replaced some wire going to the module and started fine for about two weeks. We replaced the entire module (with a used one) and started fine - for about two weeks. We replaced the key cylinder and the same result - worked for two weeks. We replaced an (I believe) ignition switch and the same result - worked for two weeks. Any thoughts? Thank you for your time and input...greatly appreciated!