This is indeed reproducible in Python 2.7. The following unittest will expose it. However, patching sys.std* to None will break `print` statements to raise AttributeError in pythonw.exe programs, though it won't mysteriously break only after printing 4 kbytes...

diff --git a/Lib/test/test_os.py b/Lib/test/test_os.py
old mode 100644
new mode 100755
--- a/Lib/test/test_os.py
+++ b/Lib/test/test_os.py
@@ -58,6 +58,19 @@
         new = sys.getrefcount(path)
         self.assertEqual(old, new)
 
+    @unittest.skipUnless(sys.platform == 'win32',
+                         'test specific to Windows console')
+    def test_print_no_stdout(self):
+        # Issue #706263: pythonw.exe will raise an IOError after
+        # attempting to print more than 4096 bytes (it silently
+        # succeeds for the first 4096 bytes and fails with an
+        # IOError: "[Errno 9] Bad file descriptor" on the 4097th byte.
+        DETACHED_PROCESS = 0x00000008
+        command = [sys.executable, '-c',
+                   'for _ in xrange(100000): print "a", ']
+        retcode = subprocess.call(command, creationflags=DETACHED_PROCESS)
+        self.assertEqual(retcode, 0)
+
 
 class TemporaryFileTests(unittest.TestCase):
     def setUp(self):