Route is not being located on my site, but works on localhost

I have a service, with GET and PUT verbs. In localhost is ok, but when I host on my site I get this error, only when I call PUT :

  

IIS 7.5 Detailed Error - 404.6 - Not Found

According to the provider's faces, this may be the route problem that is not found. See my service and the method that is called by the service.

[RoutePrefix("api/Atualiza")]
public class AtualizaController : ApiController
{
    AutorizadorContext contexto = new AutorizadorContext();
    PedidoLiberacao liberacao = new PedidoLiberacao();

    [Route("{id}/{value}")]
    [AcceptVerbs("Put")]
    public void putItensLiberacao(int id, string value)
    {
        liberacao.AtualizaLiberacao(id, value);
    }
}

The method that is called

[Route("{id}/{value}")]
public void AtualizaLiberacao(int id, string value)
{
    var lista = contexto.Liberacoes
        .Where(l => l.IdOrcamento == id)
        .ToList();

        lista.ForEach(f =>
        {
            f.FlagLiberacao = 0;
            f.AutorizouReceberAtrazado = value;
        });
            contexto.SaveChanges();
}

would be the url like this:

  

www.mywebsite.com/authorizer/api/update/1000012120/Testing