Beckett has to survive, she and him are the spark of the show - however, I think that Beckett is gonna slip into a coma for a while, come out of it and have no memory of Castle. That's gonna reset their relationship to zero and allow them to drag it out for as long as they want.
Oh, damn, I hope not. That would be incredibly lame and corny, a tiresome soap-opera cliche with zero believability. Good grief, if she suffered enough brain damage to erase the past three years of her memory, then realistically she'd have other serious neurological impairments that would probably make it impossible for her to function as a detective, maybe even to lead an unassisted life. To have her restored to perfect functionality but with the last three years of memory gone -- or even worse, to remember everything except Castle -- would be completely nonsensical.
Not to mention that resetting her character to square one, erasing all her life experience of the past three years, would be a total waste from a storytelling standpoint.