From what I've read online, there are several ways to fix the Assasins Creed IV: Black Flag save game issues. The simplest one is to make sure that you run the game with administrator privileges. To do this, simply right click the executable file, then choose the Run as administrator option.
If that didn't solve your issue, you will need to go to the application's install folder. Once again right-click the shortcut, go to Properties, move to the Shortcut tab and press the Open File Location button. In the installed location, go to the folder named Save3dmgames, then right-click any file you see there and make sure that the Read-Only box isn't checked for any of them.
Lastly, many users reported that turning off the cloud saving option in Ubisoft application did the trick. Open the Ubisoft Client, go to Settings --> General and remove the check mark from the Enable Cloud Synchronisation option. If you can't find it, disable anything that has to do with online stuff and your saved files should now be visible.
Also, I would advise you to start the game scratch instead of using the saves that you couldn't see before. The future saves that you make will remain visible.