The valve that Ignatius always refers to is his pyloric valve—a ring of muscle that controls the movement of food from the stomach to the small intestine (2.6).
As a symbol, the valve (appropriately) connects two concepts. First, it is a kind of interior ring or wheel of fortune; it's obscure openings and closings give Ignatius good fortune or bad, as his digestion determines.
But the valve is also just a stand in for Ignatius himself. Ignatius is almost all stomach anyway, and the bit of him that isn't stomach seems largely determined by appetite. The valve is both a (literal) embodiment of his stomach, and a way to link that stomach to his body's demands—most notably its sloth. Whenever Ignatius doesn't want to do something, it seems, his valve obligingly comes to his rescue. He notes, for instance:
My valve did close quite violently this afternoon when Mr. Gonzalez asked me to add a column of figures for him. (4.200)
How very convenient, right? The valve is the passage, then, from chance to appetite—the link between Ignatius's fondness for blaming fortune and his fondness for not doing much of anything. Is Ignatius's life determined by fate or by his appetite? Maybe it is not a cruel, blind god who leads him to be attacked by a parrot, for instance, but instead his own, sad, compulsive belches.