I am player one and use my skip card on player three. When their turn of being skipped passes, can I use another skip card to the same player to block them from completing their Phase on my next play?
From the rules (found here):
A player may only be skipped once per round. If player one skips player two, then player two can not be skipped until player one plays again.
So if you are player one, then sure - you can skip them again.