Thank you for your post.
When you close a file in FileMaker Go, it should update the file and toggle a flag that the file has been closed. From your description, it appears this is not happening. Therefore, either the application FileMaker Go is damaged or the database file is damaged. First try removing FileMaker Go from your iOS device, and then reinstall through the App Store/iTunes. If the problem still exists, try recovering the file on the Mac.
Keep me updated with any progress.