I forgot something: to avoid trying to file rotation at each log message, the rotation should be disabled at the first error. For RotatingFileHandler, it can be something like:
 try:
  ...
 except:
  self.maxBytes=0
  raise

For TimedRotatingFileHandler, a flag (new attribute) would be required.

I'm not sure that disabling the rotation if the first rotation failure is a good idea, but most the time if the logging system is broken, the application starts to fail randomly :-/ Anyway, the first rotation exception is still raised and so would be catched by something :-)