There is already an active bug report about this in the bug report forum, and Frontier has responded saying they are aware and investigating.
Take a look at the NPC ships attempting to land at one of these large StarPorts next time you are docking there. All of them are sitting to the right of center of their pad with thrusters pulsing back and forth. Their landing windows will eventually close and the station will begin destroying all of them for loitering! Obviously the same bug that is effecting our DCs is also preventing NPCs from docking also.
If you stick around long enough, the station will be filed with ship debris and eventually the game will hard crash your PC with a Blue Screen of Death.
A previously fully functional feature getting totally broken like this after an update has become an unwelcome pattern with this game. The DC was not even mentioned in the .03 patch notes for crying out loud!