It could be that the database is in a location where the Operating System does not allow the AIR app to write.
You should think about adding some Alert.show(error.toString()) messages in your try-catch statements to determine the error exactly.
Best to write to the applicationDirectory. This blog shows how to access the applicationDirectory using the File.applicationDirectory property.
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Greg Lafrance - Flex 2 and 3 ACE certified
Flex / AIR Development, Training, and Support Services