Why does the allergic response increase in its severity, with consecutive exposure to the allergen?
Are there more mast cells present each time?
Yes.
So the way an anaphylaxis response works is like so:
Mast cells contain vesicles of histamine waiting to be released.
Upon the 1st exposure of the allergen, antibodies are formed. These then sit on mast-cells with the two variable regions reaching into the extracellular fluid surrounding the cells. These antibodies link with the allergen spread across the two separate antibodies (think Y-Y) essentially linking them together in a chain.
When they are re-exposed BAM. These antibodies trigger a cascade response, the vesicles are exocytosed and the reaction occurs.
Subsequent exposures may or may not trigger the creation of more mast cells hence increased severity.