This seems like a fairly obvious question. Morpheus is a user, his password's about to be found out, but why can't the sysadmins (the people controlling the mainframe) change the password? Or delete his 'user account'? It's not like this is a stealthy 'hack'; they know that Morpheus is compromised. Just tell Zion 'hey, revoke admin privileges for the Morpheus user' and that way they don't have to unplug him. They probably want to rescue him still, but they can take their time knowing that even if Morpheus breaks and gives them the codes, they'll be worthless.
Zion didn't know that they needed to change the codes.
Simply put, ships can't transmit from "Matrix broadcast depth" back to Zion. They either need to get much much closer, as they do in Reloaded when they're approaching Zion control and request the defences be 'stood down' and a dock made ready.
or in Enter the Matrix where Niobe orders the ship to
Niobe: Drop down to Zion broadcast. I want this data transmitted immediately. Emergency encryption.
They can communicate indirectly by using a series of 'dead-drops' to transmit data from a ship at broadcast depth to a ship that's heading back to Zion (as they do in the animatrix short The Final Flight of the Osiris. Note that at the point that Morpheus is captured, the Nebuchadnezzar appears to be the only Zionese ship inside the Matrix, as evidenced by the lack of support offered by any other crews to his rescue.
Additionally, to withdraw from the Matrix broadcast level requires breaking contact with the Matrix (which would kill Morpheus) so they can't simply leave him in there, travel to Zion to tell them to change the codes then return at a later time and date.