This verse presents three events. The first is the passage of time. We must always remember that the Lord is infinitely patient with his children. In the most obvious case for the Latter Day Saints, his patience to effect a restoration after the loss of the priesthood took nearly 1800 years. Just as the master of the vineyard makes an effort for the salvation of the tree, and waits to see its effects, so the Lord works with his children, providing such prophets and warnings for them, and allowing them time to see if they will listen to the warning word that was sent.
The second event is the growth of new branches. This process is precisely what was hoped for, that the efforts on the tree would renew the life in it. This happens, but not to the degree that master hopes. There are those who do listen to the prophets when they are sent, but the net result is that only "somewhat" and a "a little" does Israel repent.
The third event describes the effect of the prophets on the bulk of Israel. This is the "main top" of the tree. In this analogy, this would refer to the leadership of Israel, those who maintain the status quo. while individuals, or those peripheral to the leadership might repent, the allegory is that the leadership continues in its "decay," or removal from the true way of the Lord. This is very parallel to Isaiah's condemnation of the leadership of Israel while indicating that there would be a remnant who would remain true. (Isaiah 2-5 describe the evils of the leadership, and Isaiah 10:22 discusses the righteous remnant of Israel).
Symbolic: As the allegory develops, there is an increasing distinction made in the "tree" of Israel. The "tree" may be Israel, but the trunk of the tree is never the focus of the allegory. Action occurs at the branches, or to and for the root of the tree. While the trunk remains, it is a non-entity in the allegory, save that it carries the imagery of the collective definition of "Israel."
To this point, we are introduced to the "tree" and to the branches. The branches at this point are established parts of the tree, or new (young and tender). On the level of the branches the allegory begins to relate to specific elements of Israel. The actual people who are Israel become represented by the branches, though not as individuals. Thus the new branches will be the type of people who return to God through the efforts of the prophets, and the established branches, the "tops" are those who are the established hierarchy. The trunk is only the conceptual collective image that holds together the divergent types of branches, which is the locus of the brunt of the symbolic action in the allegory.