Your Amazon Instant Video app does not find an internet connection and sometimes shuts down all together (and never recovers). Once the app shuts down it stays shut down for the duration of the time you have the television on.
The Amazon apps seems to never recover once it fails to retrieve a network connection. Sometimes after turning the TV on it takes a moment for the TV to access the local WIFI network. The workaround is to give the TV time to access the network before accessing the Amazon app. You can monitor whether a connection has been made by hitting the Vizio button on your remote and watching for the network connected/signal strength icon in the upper right hand corner of the screen. Once you have a WIFI signal you will be able to open the Amazon app and connect.