How do you save game data when playing a Unity webGl game on a mobile browser?

My Unity WebGL game runs on the mobile web browser after heavily optimizing the Audio and texture data. Saving the game data works fine on the desktop environment. But when I play the same game on a mobile browser, there seems to be no saving of game data anywhere. My code to save and load data locally is given below.

using System;
using System.IO;
using System.Runtime.InteropServices;
using System.Runtime.Serialization.Formatters.Binary;
using UnityEngine;

public class DataAccess
{
    [DllImport ( "__Internal" )]
    private static extern void SyncFiles ( );

    [DllImport ( "__Internal" )]
    private static extern void WindowAlert ( string message );

    public static void Save ( Stats stats )
    {
        string dataPath = string.Format ( "{0}/Stats.dat", Application.persistentDataPath );
        BinaryFormatter binaryFormatter = new BinaryFormatter ( );
        FileStream fileStream;

        try
        {
            if ( File.Exists ( dataPath ) )
            {
                File.WriteAllText ( dataPath, string.Empty );
                fileStream = File.Open ( dataPath, FileMode.Open );
            }
            else
            {
                fileStream = File.Create ( dataPath );
            }

            binaryFormatter.Serialize ( fileStream, stats );
            fileStream.Close ( );

            if ( Application.platform == RuntimePlatform.WebGLPlayer )
            {
                SyncFiles ( );
            }
        }
        catch ( Exception e )
        {
            PlatformSafeMessage ( "Failed to Save: " + e.Message );
        }
    }

    public static Stats Load (Stats stats )
    {
        //Stats stats = null;
        string dataPath = string.Format ( "{0}/Stats.dat", Application.persistentDataPath );

        try
        {
            if ( File.Exists ( dataPath ) )
            {
                BinaryFormatter binaryFormatter = new BinaryFormatter ( );
                FileStream fileStream = File.Open ( dataPath, FileMode.Open );

                stats = ( Stats ) binaryFormatter.Deserialize ( fileStream );
                fileStream.Close ( );
            }
        }
        catch ( Exception e )
        {
            PlatformSafeMessage ( "Failed to Load: " + e.Message );
        }

        return stats;
    }

    private static void PlatformSafeMessage ( string message )
    {
        if ( Application.platform == RuntimePlatform.WebGLPlayer )
        {
            WindowAlert ( message );
        }
        else
        {
            Debug.Log ( message );
        }
    }
}

Does anyone know whether this can be done, if so how?