Yes, the Director's PIN is carried over between scoring sessions. You can change it from the default value via the PIN menu in BridgePal Server (click on the icon that looks like two overlapping phones ,on the windows taskbar, to bring up the BridgePal Server window).
Whatever PIN you use, whether it's the default or otherwise, you still have to enter it every time you carry out a Director's function. This is deliberate, because otherwise the players at a table would be able to access director's functions if the director had previously used a function (e.g. "Change Score") on the BridgePal at their table.