Once maximum vacuum is reached and you turn the pump off does the chamber hold the vacuum or, do you have to leave the pump running for the entire stablezation process?

The pump needs to running the entire time to keep the vacuum at the fullest level.  My chambers do not even have a valve between the pump and chamber for this very reason.  As soon as you shut off vacuum, the level of vacuum inside the chamber begins to slowly go down.  You are actually only creating vacuum in the space above the Cactus Juice in your chamber and as the air flows from the point of higher pressure in the wood to the point of lower pressure in the space above the resin, if the pump is not running to maintain that lower pressure, it begins to drop and equalize.  If vacuum level is dropping, the air moving from the blanks to the lower pressure above the blanks drops off as well.  Keeping the pump running keeps the pressure above the resin at is lowest level, maintaining the proper flow from the wood.  In other words, keep the pump running for best results!