This gives me the willies. Luckily, I wasn't yet using the EC2 instance when it just up and vanished, but I doubt that Amazon knew that. What's to make me believe it wouldn't happen again?
I think I might stick with Rackspace for now.
PS and yes, I am logged in with the right account -- I verified against the confirmation email I got when I signed up.
Update: Ahhh... found the cause, and the solution! I posted on the Amazon support forum, and it turns out that it's possible to have what is called a "MASE" problem, which stands for "Multiple Account, Same Email." WTF!!
Indeed, I logged out, used the SAME email address, but a different password, and was able to log in with my other account and see my running instance.
OK, Amazon that isn't so bad I guess. Except, it's weird. And how in the world did I get another account?