How does changing the shape of ATP synthase specifically prevent the enzyme from working any longer?
If you look at an enzyme and its substrate you can also see this as a lock (the enzyme) and the key (the substrate). The key fits the lock and opens it, the substrate fits into the active pocket of the enzyme and a reaction takes place. See this figure for illustration (from here):



If the enzyme (or the substrate) changes its outer shape (this is what happens when amino acids of a protein are changed), this fit will not happen anymore and the reaction which is catalysed by the enzyme will not take place (the lock will not open).