Can I keep the speech recognizer listening indefinitely?

The Android Speech recognizer can be customized through the intent extra data. See the android documentation.

public static final String EXTRA_SPEECH_INPUT_COMPLETE_SILENCE_LENGTH_MILLIS

The amount of time that it should take after we stop hearing speech to consider the input complete. [...]

public static final String EXTRA_SPEECH_INPUT_MINIMUM_LENGTH_MILLIS Since: API Level 8

The minimum length of an utterance. We will not stop recording before this amount of time. [...]

public static final String EXTRA_SPEECH_INPUT_POSSIBLY_COMPLETE_SILENCE_LENGTH_MILLIS

The amount of time that it should take after we stop hearing speech to consider the input possibly complete. [...]

Set the EXTRA_LANGUAGE_MODEL to websearch to capture only relevant words.

You can implement onError of RecognitionListener interface like this. It is continuously listening in your activity.

@Override
public void onError(int error) {
    String errorMessage = getErrorText(error);
    Log.i(Constants.TAG, "FAILED " + errorMessage);
    speech.destroy();
    speech = null;
    StartListening();
}

private void StartListening() {
    speech = SpeechRecognizer.createSpeechRecognizer(this);
    speech.setRecognitionListener(this);
    recognizerIntent = new Intent(RecognizerIntent.ACTION_RECOGNIZE_SPEECH);
    recognizerIntent.putExtra(RecognizerIntent.EXTRA_LANGUAGE_PREFERENCE, "en");
    recognizerIntent.putExtra(RecognizerIntent.EXTRA_CALLING_PACKAGE, this.getPackageName());
    recognizerIntent.putExtra(RecognizerIntent.EXTRA_LANGUAGE_MODEL, RecognizerIntent.LANGUAGE_MODEL_WEB_SEARCH);
    recognizerIntent.putExtra(RecognizerIntent.EXTRA_MAX_RESULTS, 3);

    //if setting.SpeechEnable
    speech.startListening(recognizerIntent);
}