To what extent and in what ways do love and relationships present a method of survival in The Handmaid's Tale?
For Offred, she is able to survive her horrible circumstances because of love--love for her daughter, love for her old husband Luke, and in the end, her love for Nick.
She mentions throughout the story how at night, when she is finally alone in the privacy of her room, she is able to escape. Escape for her is remembering her life before, with her husband and daughter. Going over those memories of them, and feeling the love that existed between them, keeps her sane. It is her only refuge, her only escape, her only anchor to a world where love actually meant anything. The world that she lives in now is devoid of love, and physical intimacy was a hushed, stifled thing. It is easy, in her world, to buy into the ideologies being pushed, and doing so would make her lose her individuality. So, she clings to that love of her child and husband like a lifeline to her own identity. That love also gives her hope; she feels like she would know if they had died. She feels like her love would flicker or dim, and because it hasn't, her love gives her hope that her family is still living.
Her love for Nick is a bit different. It is more of a physical escape, a form of rebellion against their society, and a way to prove that she was indeed alive, strong, wanted, beautiful and capable of emotion. Being with him is her firm fist of defiance against the repressive system that she lives under. These moments of escape with Nick give her the sanity to go forward in the daytime and live the charade she is forced to act in order to survive; they give her the inner conviction that life really hasn't changed that much, and knowing that she can escape and be her true self later is also a lifeline to her.
I hope that those thoughts helped; good luck!