WaveSpawner in Unity

Question

i have a wave spawner script from a video i saw, since I'm fairly new to this still and its just more so a learning experience than anything really, but when spawning in the zombies im quite confused why the Wave Countdown is stuck and not counting down after i have killed them all to go onto another wave? the code for the wavespawner im using is

using UnityEngine;
using System.Collections;

public class WaveSpawner : MonoBehaviour {

    public enum SpawnState { SPAWNING, WAITING, COUNTING };

    [System.Serializable]
    public class Wave
    {
        public string name;
        public Transform enemy;
        public int count;
        public float rate;
    }

    public Wave[] waves;
    public int nextWave = 1;
    public int NextWave
    {
        get { return nextWave + 1; }
    }

    public Transform[] spawnPoints;

    public float timeBetweenWaves = 5f;
    public float waveCountdown;
    public float WaveCountdown
    {
        get { return waveCountdown; }
    }

    private float searchCountdown = 1f;

    private SpawnState state = SpawnState.COUNTING;
    public SpawnState State
    {
        get { return state; }
    }

    void Start()
    {
        if (spawnPoints.Length == 0)
        {
            Debug.LogError("No spawn points referenced.");
        }

        waveCountdown = timeBetweenWaves;
    }

    void Update()
    {
        if (state == SpawnState.WAITING)
        {
            if (!EnemyIsAlive())
            {
                WaveCompleted();
            }
            else
            {
                return;
            }
        }

        if (waveCountdown <= 1)
        {
            if (state != SpawnState.SPAWNING)
            {
                StartCoroutine( SpawnWave ( waves[nextWave] ) );
            }
        }
        else
        {
            waveCountdown -= Time.deltaTime;
        }
    }

    void WaveCompleted()
    {
        Debug.Log("Wave Completed!");

        state = SpawnState.COUNTING;
        waveCountdown = timeBetweenWaves;

        if (nextWave + 1 > waves.Length - 1)
        {
            nextWave = 0;
            Debug.Log("ALL WAVES COMPLETE! Looping...");
        }
        else
        {
            nextWave++;
        }
    }

    bool EnemyIsAlive()
    {
        searchCountdown -= Time.deltaTime;
        if (searchCountdown <= 0f)
        {
            searchCountdown = 1f;
            if (GameObject.FindGameObjectWithTag("Enemy") == null)
            {
                return false;
            }
        }
        return true;
    }

    IEnumerator SpawnWave(Wave _wave)
    {
        Debug.Log("Spawning Wave: " + _wave.name);
        state = SpawnState.SPAWNING;

        for (int i = 0; i < _wave.count; i++)
        {
            SpawnEnemy(_wave.enemy);
            yield return new WaitForSeconds( 1f/_wave.rate );
        }

        state = SpawnState.WAITING;

        yield break;
    }

    void SpawnEnemy(Transform _enemy)
    {
        Debug.Log("Spawning Enemy: " + _enemy.name);

        Transform _sp = spawnPoints[ Random.Range (0, spawnPoints.Length) ];
        Instantiate(_enemy, _sp.position, _sp.rotation);
    }

}

if anyone has any ideas as to why or knows what the problem is it would really help