It is easy to get things out of sequence when dealing with time travel stories, and part of this article speaks of an event that happened before Alex attended Kate's birthday party. Part of it comes after that, though.
Not surprisingly, Kate and Alex talk about meeting, and doing so in her time. She can make plans for tomorrow, and he can make plans for two years and a day hence.
The first effort should not be taken too seriously; it contains a serious danger, in fact. Kate suggests that Alex should call her on July 10, 2006, at 9:05 P.M. She looks at her watch, and as she writes it, the phone rings--but it is Morgan, returned from long absence and wanting to see her.
What would have happened had it been Alex?
The first problem is that she is writing a letter she will not send at least until the next day--she must drive to the lake house to put it in the mailbox there. Thus before she mails it she will know whether he called. As she mails the letter, though, she puts an end to this timeline, and in this timeline Alex never got the letter so he could not have called her. She thus already knows that he did not call her; does she still mail the letter to suggest he do so? Supposing, though, that she does, and that he was not killed at Daley Plaza, it is likely that he will call her. Thus before she mails the letter suggesting that he call, she receives that call. But then, does she still mail the letter?
Does the magic end when they meet in her time? This is a significant complication as well. If they manage to meet because of the letter before she sends the letter, and if their meeting ends the magic the letter will never be sent. However, if the magic is created to bring them together, it is unlikely to last beyond that moment--unless we believe that once they move into the lake house together they can continue to communicate across time as long as she puts letters in the mailbox for him and he pulls them out two years in the past.
In this regard, it is fortunate that Alex died at Daley Plaza. Had he lived, this would have been very complicated.
Perhaps she realizes the problem; perhaps it was just that the fortuitous timing of Morgan's call prevented her from realizing that her call waiting would have alerted her to the other caller. In any case, they decide to try again. She picks the restaurant, and he makes the reservation. However, he died at Daley Plaza that spring, so he is not there for dinner that autumn. It shakes her, and she decides that she is living a dream, a fantasy, that cannot be real.
She ends the relationship, stops picking up his letters or sending any of her own, and when Morgan calls decides she will accept the mundane reality instead of the wonderful fantasy. He moves into her apartment.
A year passes during which they have no contact. It is easy to overlook this, but nothing in the film happens in 2005 or 2007. In 2005, Alex is working with his brother; in 2007, Kate is returning to the mundane life with Morgan. This is important in part because 2005 is the time during which Kate lives in the lake house, and it would be at best difficult for Alex to pick up letters she sent from 2007 during that year without being noticed at some point and disrupting everything; thus the breakup is necessary to their relationship.
It is more peculiar that she makes no effort to learn what happened to him. She apparently assumed that his life took him elsewhere and he never looked back. This is a reflection on her own self-image, perhaps; but then, we are usually surprised to learn that people we knew have died young, so she did not consider the possibility at the time. Probably she did not want to know why he did not show; she expected it to be a negative reflection on her.
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