I just asked the same type of question a little while ago, and this is what someone said: you could use a program like iexplorer, ifunbox, diskaid, itools and back up the documents and profile folder of that game most of the times the documents folders keeps the save games. So you just delete the old and download the new and paste that folder again and you should have your progress You should also make sure the game doesn't have iCloud backup first, though.
If you are jailbroken, I HIGHLY recommend DataDeposit, I've been using it since release and it's filled with all my saved data since then. It uploads save data to a Dropbox account.