Instance IDs are only valid within the same session. In stead I'd suggest saving the path of the GameObject.

using UnityEngine;

public class GameObjectUtility
{
    public static string GetPath (GameObject gameObject)
    {
    	string path = "/" + gameObject.name;
    	Transform transform = gameObject.transform;

    	while (transform.parent != null)
    	{
    		transform = transform.parent;
    		path = "/" + transform.gameObject.name + path;
    	}

    	return path;
    }

    public static GameObject GetGameObject (string path)
    {
    	return GameObject.Find (path);
    }
}

Edit: Since you're working with GameObjects with non-unique names, you could alternatively set up a custom asset to store serialized references to your GameObjects.

Custom asset handling:

1. Create a ScriptableObject derived class which stores your data (groups and GameObject references in your case).
2. To create a new asset of your type, use AssetDatabase.CreateAsset (new YourAssetType (), "Assets/Path/To.asset");.
3. To load your asset at editor time, use myAsset = AssetDatabase.LoadAssetAtPath ("Assets/Path/To.asset", typeof (YourAssetType)) as YourAssetType;
4. When you have made a change to your asset, use EditorUtility.SetDirty (myAsset); to serialise them to disk.
5. To access the asset data at runtime, make a public variable in the script needing access to the type of your asset and drag-drop the asset from the project view to that property in the inspector.