If it is using sessions to store the 'w3t_visit' and php is running with register_globals set to 'off'*,
some things have to be done in a different way. It has happened to me too and the result is that the value is set only the first time (that is if you use session_register).
I'm not sure if this is the problem here, but it is definitely in 5.5.1 with register_globals=off.
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* register_globals=off => you must use $_SESSION => session_register will not work.