I think Corion called it right. From the docs (my emphasis):

The current position of the StreamReader object is not changed by Peek. The returned value is -1 if no more characters are currently available

That suggests .Peek will return -1 when there is nothing currently available. Not when nothing more will ever become available (in a microsecond from now).

Your fix is probabaly to use the "standard c# idiom":

            using (StreamReader sr =  ... ) 
            {
                string line;
                // Read and display lines from the file until the end 
+of 
                // the file is reached.
                while ((line = sr.ReadLine()) != null) 
                {
                    ...
                }
            }
        }
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