More code would be helpful, but you likely need to put this in your show method.

public void show() {
    Gdx.input.setInputProcessor(yourInputProcessor);
    // This should keep it from exiting.
    Gdx.input.setCatchBackKey(true);
    ...
}

More code would be helpful, but you likely need to put this in your show method.

public void show() {
    Gdx.input.setInputProcessor(yourInputProcessor);
    // This should keep it from exiting.
    Gdx.input.setCatchKey(Input.Keys.BACK, true);
    ...
}