This is a pretty common problem for PS3.... not just this game, but for many online games.
DCUO on the PS3 froze constantly, it was so bad that Sony had to make fixes for the game to compensate... you'd think Sony would understand their own system limitations enough to stop it from happening.
The great part about FFXIV is you can adjust how many effects the graphics engine will attempt to run, so I recommend going into your settings and toning down effects a bit, especially for other players, pets and minions.
It seems like this problem was directly related to the graphics overloading the PS3's processors on that game, so it's probably similar to what you're experiencing. I have already done this on my game, but for different reasons.... I just want the mobs to appear sooner when I'm doing FATE's so this will help fix both of these problems.