The impersonal pronoun "Il" is the subject of the first clause and the verb « se passer », une journée is the direct object, and as it follows the verb, there is no agreement with the object.
A couple of links:
Conjugate reflexive verbs in the present tense in French (Le Présent)
My understanding of the translation is something like "Not a day goes by without her making (doing) the (la) face"
So "elle" belongs to the subordinate clause introduced by the relative pronoun "que".
"ne" is expletive.
This is how I see it -- I look forward to others' comments though.
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