Well, I'm sorry to bring this up again, but the problem persists
with Python 3.1.2 (x86, Windows XP). The difference with the
test script behaviour is that now it doesn't break every time.
Perhaps this is the reason I said the problem was gone.
In fact, now that I run the aforementioned script I may get

worked so far
but not here it didn't

and some other time I may get

worked so far
Traceback (most recent call last):
  File "test.py", line 23, in <module>
    test_handshake(address, False)
  File "test.py", line 17, in test_handshake
    ssl.do_handshake()
  File "C:\Python31\lib\ssl.py", line 327, in do_handshake
    self._sslobj.do_handshake()
AttributeError: 'NoneType' object has no attribute 'do_handshake'

and the outcome is unpredictable. It may work many times in a row
and it may break many times in a row.

If this is of any relevance, I've had pywin32-2.14 installed since.