First you need to add a unique post ID to each of your posts:
<div class="entry masonry-brick" id="{PostID}">...</div>
The documentation mentions requesting the like status once the new posts (or new page) has been appended / loaded:
function( newElements ) {
var $newElems = $( newElements ).css({
opacity: 0
});
// Create Array of $newElems IDs
var $newElemsIDs = $newElems.map(function () {
return this.id;
}).get();
$newElems.imagesLoaded(function(){
$newElems.animate({
opacity: 1
});
$container.masonry(
'appended', $newElems, true
);
// Let's just see what we have, remove console.log() if working
console.log($newElems, $newElemsIDs);
Tumblr.LikeButton.get_status_by_post_ids($newElemsIDs);
});
});
I hope that points you in the right direction.