Get a copy of the SanDisk Memory Zone app to see which apps are hogging your Fire for application size space as well as memory hogging. Then clean out the ones that are resource hungry. I agree a full cold boot every week is helpful to clean up some items
Another good app to get is a startup cleaner so YOU decide what apps start up in the \
boot sequence not the ap.
no need to completely shut it down when you are done though, just tap to put it to sleep if you are going to use it during the day.
I only shut down all the way every so often