I was able to reproduce the notification glitch occurring with the modified
script after modifying the value of HIGH in the scrip, saving and running the
script.
Each time I do that, nothing happens until the HIGH value is reached. When
the HIGH value is reached, the sound is played and the visual notification is
displayed as expected. After which, the "Battery OK" notifications are
porperly displayed after every interval.
Note that the notification does not last more than a second, while the
notification from the battstat-applet is persistent until the user clicks on
it.