Metal Gear Solid 5: The Phantom Pain is having an issue with save data getting lost. And this bug is still active on consoles. On PC there is a fix for that. You can see a video for that below.
For PC, the solution is to first backup your existing save game files and then move them back again after you had synced Steam Cloud. But in gaming console there is no direct solution and that is why this bug is annoying a lot of players. This critical bug is already addressed by the game developers and soon they will be working on a patch that will resolve this issue. But here you must backup your current save data first. The game is just having issue with reading this files and this looks like a problem with creating or recreating the game profile.
In PC this issue was fixed just by moving the save game file first and then turning on Steam Cloud Sync. This created a new profile and then overwriting those files with your old save game data solved this issue. But in console this process does not seem to be working well.
To resolve the save data bug, the game developers will be releasing a new patch in coming time. This patch will help players to get their game working as it was before. Konami had already mentioned about a new patch to fix this problem on this link. Their development teams are working on the same and the patch will add a fix to solve this problem. This save data bug has cost many players the amount of level they had completed.