Why does Calvinism need the doctrine of Perseverance of the Saints if it believes in Unconditional Election? As I understand it, Unconditional Election means that God has already chosen who will be saved. 


  Unconditional election is God's choice to save people regardless of their sin or any condition.


Why then is it necessary for the doctrine of Perseverance of the Saints to reiterate that salvation cannot be lost? Isn't that already part of Unconditional Election? It seems to be repetitive.
When the five points of Calvinism are looked at as distinct entities, then there does seem to be a bit of redundancy in there.   Part of the reason, though, for that is that the five points are emphasizing bullet-point highlights of a comprehensive theology, and they were done so as a retort to the five points of Arminianism, which follows:

Five Articles of Remonstrance (summarized)


  
  God has elected to save any person who responds to his grace.
  God's saving grace is offered freely to all, but is only sufficient for those who respond.
  All humans are sinful and incapable of being righteous. However, God has provided grace to enable them to respond to him.
  God's grace enables all good works, but human beings have the capacity to resist God and choose evil.
  God's grace and the power of the Holy Spirit enable believers to overcome sin if they are willing to persevere.
  


As it's presented in a fashion that aims to address specific issues, its presentation is naturally going to appeal to certain "common themes" while framing the underlying theology with certain key points in primary focus.  The perserverence of the saints specifically counters the fifth point of Arminianism.

Calvinism contends that because the saints are neccessarily new creatures (see Total Depravity/Total Inability), who have been elected solely according to God's will and not their own worthiness (see: unconditional election), and saved definitively by the shed blood the Christ (see: Particular/Limited Atonement) and effectively through the regeneration of the Holy Spirit (see : Irrisistible Grace), then those saints will necessarily, perservere to the end of their lives.   

So, you're right, on first pass it does kind of seem redundant or unnecessary, but it's more of an extension of the preceeding points, and it specifically addresses a contrasting view.