Kate Beckett cannot die! She is the main character in the series. Castle's character is theorized criminal acts and behavior for Beckett to solve them. So Beckett is the other half of the puzzle. Even though Castle clarified his love intentions for Beckett at the end of the third season, its not going to blossom. Because if both of them falls head-on, then the Castle and Beckett police relationship will fizzle. They will still stay platonic and continue investigating. What I wish for the upcoming season is that Beckett solves her mom's case and conclude this long over-bearing episode. Once that is concluded then the writers can start looking at other angles - perhaps more sinister and suspending. Look Castle is a writer and writers do not just look at normal street crimes...they always want to look at something perhaps more covert and has a touch of conspiracy twist to it.
She shouldn't die, but she should give up on the death of the mom thing. When plots drag out like this, interest lags. It is a much better show when she and Castle are playing off each other tracking a single episode murder.