They most definitely have multiple instances of the app running around the world, which synchronize data with each other, which is why you've never been unable to buy something. It's highly unlikely that all their instances would be down or overloaded at the same time.
Also, they most certainly don't have a single logical database. They use all kinds of things, including SimpleDB. You think product information is stored in the same database, or even in the same away as customer information?
>What I mean by that is that within Amazon, all small pieces of business functionality are run as a separate service. For example, this availability of a particular item is a service that is a piece of software running somewhere that encapsulates data, that manages that data.