There is a specific, infamous bug in SE3 involving the "Authenticating" message followed by the fail. This usually happens in the missions.
If the issue persists, the problem might not be Sniper Elite 3 at all, but rather a broader instability in your network path to Steam. Data sent from your device to Steam's servers must pass through many routing nodes; if you are far from the server, the path will be longer and more likely to experience jitter or packet loss. sniper elite 3 connection to the game failed top