At the end of The Notebook, we see Allie and Noah dead together holding each other's hands. I think that Noah had been trying for a couple of times to let Allie remember everything permanently. But the expected "miracle" did not happen a single time, and every time she lost everything. Now my question is how did they die together? As this was not the first time Allie forgot everything, I don't believe it was a serious physical problem that can cause death. Apparently, Noah was also not sick, although he got a heart attack. But I believe it was out of his sorrow for again losing her. He was there to help Allie. So how come they died together? Did they commit suicide?
Allie asks Noah if he thinks their love is so strong that it can grant miracles and he says yes, which is proven by her memory returning against all odds. She then asks if their love is so strong that it could take them away together, which would be another miracle. Their dying in the next scene shows that their love was so strong that it granted the miracle of them dying together. They didn't commit suicide and there was no medical problem, it was just a miracle. It's a really cheesy plotline, but that's what was intended.
No, they didn't commit suicide. They just died together. In a scene before that, Allie askes Noah if their love has the power to grant miracles, and Noah tells her yes. She also asks him if their love can take them away together (die together). So they just wanted to imply that their love was so strong that they died together. Although, in the original novel, on which the movie is based, only Allie dies and Noah continues to live at the nursing home. It also has a sequel called "The Wedding".