You should close your FileOutputStreams, as well as your ArchiveInputStream, preferably in try-finally blocks or try-with-resources. Right now you have a major resource leak, and if your archive contains too many entries you will run out of file handles.
I think the issue with your original code is that FileUtils.copyInputStreamToFile closes the source input stream. I think this is a mistake, because a) it's not documented, and b) library calls shouldn't close resources that are passed as input arguments - it's the responsibility of the code that created a resource to close it again.
Anyway, your original code would work if you'd wrap the ArchiveInputStream in an CloseShieldInputStream. The resulting InputStream behaves just like the wrapped ArchiveInputStream except its close() method does nothing. As a result, FileUtils.copyInputStreamToFile would still do the correct copying but it wouldn't close your ArchiveInputStream.