In most cases the elephant* in the room is your DB - it doesn't matter where your stateless application servers are, if your stateful DB goes down you're in trouble. It's also often 1) the hardest to replicate, as replication involves tradeoffs - see CAP theorem & co and 2) the most expensive, since it needs to be pretty beefy in terms of CPU, RAM and IO - all very expensive on AWS.

*: https://commons.wikimedia.org/wiki/File:Postgresql_elephant....