Users were reporting autosave and manual save issues, but the problem seems to have been fixed on the server side.
UPDATE: The issue seems to have been resolved.
From Sony, "Some players may have been encountering an issue with The Last of Us which affected the autosave feature, which can result in a loss of progress in the single-player campaign. The team at Naughty Dog has been diligently investigating as soon as we heard from our community, and we have determined the cause to be on servers for The Last of Us which were capturing player statistics. We have made a change to ours to address this issue. All players should quit any game in progress out to the XMB and restart The Last of Us. All players can now enjoy single-player and online multiplayer matches as normal."
'The Last of Us' just released today, and by accounts the game lives up to the hype. The game's critical reception has been nothing short stellar, and many individual reactions are following suit. That said, many users are reporting a bug that did not crop up in review copies.
The bug may be related to the day one patch, but the cause is not yet known. The game features an autosave as well as a manual save. Unfortunately, over the past day, users are finding the autosave unreliable. In some instances, where selecting continue has failed, a manual load has been successful. Likewise, users monitoring the game's autosaves, have found limited success using manual saves.
As it stands currently, the most reliable way to play without losing save progress, is to play the game offline. Signing out of PSN, or just being disconnected altogether is the best method.
Presumably, the Naughty Dog is scrambling to develop a fix, and one that does not spawn further bugs, which is normal for this kind of game-breaking launch day situation. This PSA will be updated once the issue is resolved.
Author: Brian Hoss