I am very new to all Orchid business too but I got my Orchid on 24th of March (4 months on Thursday!) and it is still blooming and new spike started to grow a week ago. If it will keep growing as quick as it is now I believe new spike will bloom before old spikes loose all the blossoms. I can't imagine cut flower to stay fresh for 4 months though.
But in the end of the day it is up to you if you want to cut it.