During the download of an app, or after the app has finished downloading, it will automatically disappear. It will be recorded in the Play Store as being "Installed" but it is nowhere to be found on my device. What is going on!?
The app is not being removed from your device, but it does get removed from the launcher. This means that the icon to start the app has been removed.
You can add the icon back again by going into "All Apps" and find its icon, then long-press it to drag it onto a home screen or folder.