I cannot verify the update part of your question.
I use the application's Documents all the time and after an update that is untouched, so I can still use any files added to it in a previous version.
For the reinstalling (i.e. first delete the app, then re-download it from the AppStore and run it) there is obviously no such way, unless you consider what ravi.p suggested in his comment (adding it to PhotosAlbum). That would beat the entire purpose of a reinstall. If a user deletes the app they want to delete all its data. That's why the warning dialog specifically makes that clear. If you could circumvent this would beat the intention, wouldn't it?
The previous Documents directory isn't changed in this case, it is deleted and on the reinstall a new one is created.
I didn't check it recently, but I believe even the full path of the Documents directory doesn't change after an update, including the hashed part that is created by the sandboxing mechanism. My guess is that you're either confusing something with the update process or simply get a different file name in the newer app version.
Edit:
Okay, so apparently the application's folders can change on an update, at least according to what you further explained in your comment. :)
Then I am wondering how you can find your sqlite file again, but in ay way there is an easy solution to your problem:
Do not save the full path in your database. That is bad practice anyways, since the method you already used to get it in the first place (after downloading the file) is meant to be used for accessing the folder. So you only save
[response suggestedFilename]
in your database (going from your posted code).
In places where you need to access the file you then simply rebuild your path in just the same way you do in the first line of code you posted.
You can even write a convenience method for this in some place (a model class or the class taking care about DB access).
And by the way: Again, updating and reinstalling are two different things, especially the process in which Xcode copies your development build onto your development device is a different one from how users ultimately update your app from the store.