It really should be noted that Sparks' book really speaks to the power of love. I am not sure you will get very far in suggesting that the book depicts love in a negative manner. (Thousands of Kleenex boxes will prove compelling in this argument.) I think that love can be seen to be a painful experience, something that can evoke some of the negative elements. Yet, I don't think that the primary motivation of the work is to suggest love is a negative experience.
One of the most negative effects of love as shown in the novel is the pain that seems to be intrinsic to it. The idea of pain is something that Noah experiences in more detail than Allie. It is she who does not respond to his letters, and while she is not to blame for this because of her mother's actions, there is a certain pain that resides in Noah in never being able to experience the reciprocity of love and the emotions he invested in it. This same element of pain is evident when Allie's Alzheimer's ends up wiping out her memory of him and their love. This brings out another negative effect of love in that memory plays a role in love. When that memory goes, it is painful to experience. It is the memory of their love that withstands the 14 year separation. Memory ends up playing a large role in what drives and sustains love. The implication here is that when memory is gone or forgotten, love goes with it. Given their condition in love, the only chance for love exists when Allie's memory fades back into existence from a condition where it is slowly eroding. This can be seen as both a reflection of the endurance of love, but can also seen as a painful and negative element of love, for
Noah's hope resides in the glimmer of brief memory that Allie has. In this, there is a negative and painful element of love. Love is not shown to be negative, but there are painful and negative conditions or circumstances within it.