The problem is indeed persistent, I never could get the queries to be
redirected to the secondary while passing by the mongos.

The scripts are very simple: it is just looping queries. Here is two
examples that does the same thing, one in java and the other one in C#:

JAVA:
try {
Mongo _mongo = new Mongo("osmngs01", 27017);
_mongo.setReadPreference(ReadPreference.SECONDARY);
DB db = _mongo.getDB("AAAAA");
if (db.authenticate("XXXXXXX", "YYYYYYYY".toCharArray()) == false) {
String message = String.format("Initialization Error: Failed to
authenticate to %1$s.", "osmngs01");
System.out.println(message);

DBCollection coll = db.getCollection("players");
for(int i=0;i<10000;i++)
{
DBObject player = coll.findOne(new BasicDBObject("s_nintendoID",
Integer.toString(i)));

System.out.println("index: " + i + " players: " + player);

String message = String.format("Initialization Error: Host %1$s does not
exists. Message: %2$s",
"osmngs01", ex.getMessage());
System.out.println(message);
String message = String.format("Initialization Error: Cannot connect to
host %1$s:%2$s. Message: %3$s",
"osmngs01", 27017, ex.getMessage());
System.out.println(message);

AND C#:

string connectionString = "mongodb://XXXXX:YYYYY@osmngs01/?slaveOk=true";
MongoServer mongoServer = MongoServer.Create(connectionString);
MongoDatabase mongoDB = mongoServer.GetDatabase(MONGO_DB);
MongoCollection<BsonDocument> documents = mongoDB.GetCollection("players");
Random rndNb = new Random();
for (int i = 0; i < 15000; i++)
{
int iPlayer = rndNb.Next(1, 400000);
try
{
var query = Query.EQ("s_nintendoID", iPlayer.ToString());

BsonDocument bsonPlayer = documents.FindOne(query);

catch (Exception exc)
{
System.Diagnostics.Debug.WriteLine(exc.Message);

Simon