The novel ends with Bella and Edward at an "impasse" – they're in a disagreement, and neither is budging. It's a deadlock.
Let's take a step back and think about what has happened. First of all, the obvious: Edward’s warnings to Bella have proven true. She does get hurt because of her involvement with him (if she hadn't been with Edward, James wouldn't have considered her to be an exciting human to hunt). And Edward would rather leave Bella than see her hurt because of him. In the hospital, Bella panics when she realizes that he's "trying to talk himself into leaving [her]" (24.185).
Second, Edward is determined for Bella to remain human. When the evil vampire James bit Bella, without intervention, Bella would have naturally become a vampire herself. Yet Edward wouldn't allow it. To save her human life, he risked losing control and killing her in order to suck the venomous blood out of her veins.
Third, Bella has become 100% devoted to Edward at this point. She nails her feelings when she says, “You are my life. You are the only thing it would hurt me to lose” (24.203). By the novel’s close, she’s determined to become a vampire.
What does this all mean? Well, it means something has to give. We've got a set of incompatible circumstances on our hands, and in order for Edward and Bella's relationship to work out, there needs to be some kind of change. Bella knows a change is coming soon. In the last scene of the novel Edward says, “I will stay with you – isn’t that enough?” and she replies, “Enough for now” (Epilogue.204). In other words, the "impasse" can't go on for too much longer.
In fact, we've seen this sort of "inter-species love affair" before, and in every case, if the lovers want to stay together, one of them needs to change to be like the other. Here are a few familiar examples: