Ever since the latest update, well actually since the old version started asking me to update, the amazon appstore has been in the top 2 apps for battery usage. I don't remember this being the case before.
Just me?
I haven't had it with Amazon Appstore but I've had it with random apps here and there. Generally something gets hung up in the app and keeps it running in the background. I've found that clearing the cache (and in some cases clearing data) will fix it.
Good luck!