I happened to hit an object reference limit that exists in the Java VM of Android. If you load a bunch of files from Native Code without returning to Java at any point in between, the VM doesn't have the opportunity to clear up this references, and you end up getting an exception when the referenced objects reach 512.
The solution to this, according to online documentation, is to use the PushLocalFrame/PopLocalFrame functions. So in Android_JNI_FileOpen you'd have to open with:

mEnv->PushLocalFrame(10);

and before each return:

mEnv->PopLocalFrame(NULL);

I've tested this solution in my project and it seems to be working fine (see http://mdqinc.com/blog/2011/08/sdl-under-android/ for reference).