Trouble with Vuforia objects - first object recognizes but not second one

Here's the situation:

Using Vuforia 6 I have set up two different real-world object targets. One of them is a car and the other is a plane.

On Android when I first start the app whichever Vuforia sees first is the only one that will be recognized. So if I start the app and put the car in front of the camera the car works, but if I remove the car from view and put the plane in sight nothing happens.

If I start the app with the plane in sight, the plane works correctly but then the car won't work.

It doesn't seem to matter if I set Vuforia to recognize only a single object or 2, or 4 simultaneous. Has anyone else experienced this and tackled it?