Leave open a StreamReader in Unity c#

I am developing a game in which I need to retrieve data from a stream (that hasn't end).

I have a class called StreamingChannel which creates the streaming channel

   public StreamingChannel (){
 
     //stuff to set the stream
 
     webResponse = (HttpWebResponse) webRequest.GetResponse();
     responseStream = new StreamReader (webResponse.GetResponseStream (), encode);
     }

and to read from it i have this method

 public string Read(){
 
     try{
         string jsonText = responseStream.ReadLine();
         return jsonText;
     }catch(ObjectDisposedException){
         return null;
     }
 }

I perform the reading every tot secs with an InvokeRepeating and I do that for the whole game.

It works great except that for the fact that my stream lasts for about a couple of minute. After that it throws an ObjectDisposedException.

At first I wanted to restore the connection but I didn't manage to do that without reinstantiate the whole connection. In this case the problem is that the game lags for about a seconds. So how can I tell the StreamReader that has to leave open the channel?

ps I cannot use the constructor

 public StreamReader(
 Stream stream,
 Encoding encoding,
 bool detectEncodingFromByteOrderMarks,
 int bufferSize,
 bool leaveOpen)

because it has been introduced in the version 4.5 of the .NET Framework, and Unity doesn't support that.

Thanks for the support!