iOS 10 now has power saving requirements and will not allow background tasks to function to save battery. For example, a VoIP app can no longer use a polling strategy to stay awake. The new recommended way, according to Apple (https://developer.apple.com/library/content/documentation/Performance/Conceptual/EnergyGuide-iOS/OptimizeVoIP.html), is to use VoIP silent push notifications to wake up the app and do the work.
When the app is in the foreground, all works fine.
The issue is with the call to "setTimeout" in the iOSExec.nativeCallback function. It makes sense that if Apple is trying to minimize background execution to save battery, then they would limit the use of the setTimeout feature.
This issue is fixed by changing the iOSExec.nativeCallback function to call the cordova.callbackFromNative function directly without a setTimeout wrapper. I understand that removing setTimeout is not an elegant solution and may cause deadlocks. Maybe a new argument isBackground or something to that effect.