Where does The Phantom Pain store its save-game data on PC?

The Phantom Pain stores its data on two locations, the first one contains exclusively The Phantom Pain data, and the latter is shared with Ground Zeroes. (For purposes such as importing the save data to Ground Zeroes) Where the UserID matches the one of the Steam Account that has the save data.

• The Phantom Pain save data can be found under Steam's directory Steam\userdata\UserID\287700
• Ground Zeroes and The Phantom Pain data can be found under Steam\userdata\UserID\311340

You can also check the folders using the Previous Versions on Windows, by doing Right click -> select properties -> Previous Versions tab and you can see a number of backups made by the OS that you can browse. It stores the changes through the day, but then it keeps a single, latest daily one.

Might differ depending on your setup, but the default location should be 'Steam\userdata\*\287700'

Might be worth pointing out also that there's been a patch released now that addresses the mission 29 and 42 bug.