InputStream input = buffer.asInputStream();
ObjectInputStream oi = new ObjectInputStream(input);
Object obj = oi.readObject();
Your "server read method" is only reading one object. If it is called multiple times, you will get an error since it is trying to open several object streams from the same input stream. This will not work, since all objects were written to the same object stream on the client side, so you have to mirror this arrangement on the server side. That is, use one object input stream and read multiple objects from that.
(The error you get is because the objectOutputStream writes a header, which is expected by objectIutputStream. As you are not writing multiple streams, but simply multiple objects, then the next objectInputStream created on the socket input fails to find a second header, and throws an exception.)
To fix it, create the objectInputStream when you accept the socket connection. Pass this objectInputStream to your server read method and read Object from that.