Here there are related: http://www.ps3trophies.org/forum/bioshock-infinite/193363-trophies-stopped-popping.html
I didn't read all to know if there are solutions.
Edit - More info.
"Note on trophies not unlocking: Some users on the forums, particularly those who have the digital version, have encountered a serious issue where none of the trophies in the game will unlock despite the requirements being fulfilled. This seems to happen only when the player is offline on PSN. Upon signing in, the trophies start unlocking again. The first trophy you should unlock is Written in the Clouds, so back up your save just before it is meant to unlock, and then if you don't receive this trophy when you should, quit out of the game completely and delete your game data. Restart the game again, install Patch 1.01, and hopefully this will resolve the issue. If it still doesn't work, try deleting the game from your hard drive and re-downloading it again."
