Does an organism have only certain antibodies for life?
Are these the only B-cell types you will ever have? Or can the body generate new types of B cells, with new antibodies to deal with newly encountered threats?


New B cells are constantly formed throughout one's life; the B cells that are present in the newborn are constantly supplemented by newly formed B cells.


  ... there is no statistical difference in the rate of production of new immature B cells in the marrow of young and old animals. In total, our results confirm previous work showing that mature B cells in old mice have a slower turnover, but more importantly suggest that the defect in mature B cell turnover is not due to a decline in B lymphopoiesis, but rather an inability of the newly made cells to replenish the peripheral compartments.


--Aging and developmental transitions in the B cell lineage. 

But the second part of your question seems to have a misconception.  The newly-formed B cells have no relationship to newly-encountered threats.  No matter what new pathogens you encounter, your newly-formed B cells don't reflect them; they are formed randomly, and it is only by chance that any particular B cell might be able to react with a new threat.  Fortunately, there are so many B cells that the chance of at least a few reacting is very high, even though only a tiny fraction of the whole B cell population can do so. 

Although new threats (mainly) require new B cells, repeated threats don't -- once a B cell is stimulated the first time, it undergoes a pathway that functionally makes it longer lived and more effective, so that on repeat exposure these optimized B cells are called in and there's much less need for the new naive B cells.