Giving your creature indestructible can be a lifesaver if you need other stax pieces (I am assuming if you play Boromir, Warden of the Tower , you are playing a stax deck) to stay alive, or if you just want to beat down someone and survive a board wipe
Its also a Faerie, meaning that if your deck likes Nightveil Sprite, it might well want a second copy
Ive suffered this problem more than once
At this point you can invest in cards like Ashe, Princess of Dalmasca, Combat Tutorial and Adventurers Airship to help keep your hand fueled, and even more cheap interaction like Youre Not Alone, Ice Magic and Syncopate to force through the win
For example, check out this Mayan Calendar MTG card that makes you lose 1,000 life