I have the same problem. Not only on AFCAD Airports.
The planes just dissapear sometimes in the air sometimes while waiting for clearence.. and so on. It´s really annoying
when you have have 3 planes taxiing to the runway
and finally 1 makes it into the sky.
It seems this does not happend with the default traffic.
I think I allready tried everything.. I surrender 

I'm having the same problem but only with AI float planes and 'water' surfaces. these are more discriminating in AF2 than regular (land) airports.

The smart money (those who have successfully built and added flying AI planes)  tell me it's to do with the Hold Short nodes. Hold short positioning is critical (within 225') and also, IFR traffic will not receive clearance (thus will sit there and disappear) if the Hold short node is not included.

Lee Swordy refers to the Hold Short Node as "essential"

bill

Reference cited: AF2 Readme
"Note that hold short distance limits are only crucial where AI aircraft actually enter the active runway for takeoff. AI enter a runway at the taxiway entrances closest to the ends of the runway. Hold-short nodes at other locations along the runway will not normally be used for AI entry

Hold Short Nodes Hold-short and ILS hold-short nodes are special nodes that cause FS to draw hold-short markers on the taxiway. The hold-short node is also an essential checkpoint for ATC takeoff clearance.

Hold-short nodes create visible hold-short bars on the taxiway, which you can see in AFCAD if you zoom in close. AFCAD automatically orients the marker so the dashed-line side faces the runway. If for some reason the program has not oriented it the way you want then you can flip the marker to the other direction using a checkbox on the Node Properties Window.  ATC also uses these nodes as checkpoints for takeoff clearance.  Note: if hold short nodes are too far from the runway it can cause AI to freeze at the runway, see Hold Short Node Limits."