I am seeing the same thing here, in 2010, if I use a tool palette tool to start the DoorAdd command. If I type DoorAdd at the command prompt, it "remembers" the last offset dimension I typed into the Design tab of the Properties palette.
If you look at the Door tool properties, there does not appear to be a property for the Offset, if your Position along wall property is set to "--" (which means to use the default value, as last set in the Properties palette). You will find, however, if you set the Position along wall property to Offset/Center, an Automatic offset property will appear, and it will be set to 6". Change this to 4" (or, for maximum flexibility, change it to "--" using the dropdown list), then, if you want, change the Position along wall property back to "--". Now when you use this tool, the automatic offset will be set to 4" (or it will use whatever the current default value, if set to "--"), provided that the Position along wall property is set to Offset/Center on the Design tab of the Properties palette. Do this for each of your Door tools and you will be good to go.