your checkbox does not have a checked value. Change:
<input <?php if (!(strcmp($row_rsGetUnapprovedFreelancers['Authorised'],1))) {echo "checked=\"checked\"";} ?> type="checkbox" name="Approved_<?php echo $RepeatSelectionCounter_1; ?>" id="Approved_<?php echo $RepeatSelectionCounter_1; ?>" />
to:
<input name="Approved_<?php echo $RepeatSelectionCounter_1; ?>" type="checkbox" id="Approved_<?php echo $RepeatSelectionCounter_1; ?>" value="1" <?php if (!(strcmp($row_rsGetUnapprovedFreelancers['Authorised'],1))) {echo "checked=\"checked\"";} ?> />
also change:
$WA_fieldValuesStr = "1";
to:
$WA_fieldValuesStr = "".WA_AB_getLoopedFieldValue("Approved", $WA_multipleUpdateCounter) ."";