Whenever you receive a snap, Snapchat stores them temporarily in /data/data/com.snapchat.android/cache as jpg.nomedia files. They are able to be accessed if snaps haven't been opened yet (and for some reason some just tend to stay there long after the message has been viewed).
When a Snap is opened, the app deleted that cache of files. So it's likly that if you have already viewed them, they have been deleted.
That may not always be the case (as I managed to dig up some old snaps last night), but it's how the app functions.
There's an app called Snaps that can fetch whatever is in the temp cache folder and save it as jpgs. If you have root it's worth trying to use that app (the apk can be downloaded off Github somewhere).