How do I play late game Irelia?

How do I play late game Irelia?

How can I be an affective player with Irelia in late-game and teamfights?
When chasing down enemies or 1v1'ing I feel like she excels throughout the
whole game. During teamfights, however I target the squishy champs, and I
usually kill one before I die. Sometimes if I don't get a kill or without
me there after I die, my team loses the teamfights, which often costs us a
few towers or even the game.
I feel like with Irelia I'm doing really well and helping me team win, but
as soon as we hit teamfighting phase I just hit a wall, and I'm either
trading 1:1 or dying more than I kill. I feel that I should be playing
this way since Irelia is an assassin, sorta, but I feel like I'm not
benefiting from it late game. So how can I play her better during
late-game and teamfighting? All help and tips is appreciated!