It seems to me that the problem comes from the cinematics cut scenes.
I have contacted Square Enix .
Support page is here :
http://support.na.square-enix.com/contacttop.php?id=1161&la=1
But don't get too excited , here is their (automated?) response :
Dear Customer, Regarding your request for console support. Please find your answer below.
Most problems can be resolved by deleting the app and downloading the game again from Itunes. You will not be charges for re-downloading titles you have purchased. As long as your model ipad/ipod/iphone is supported, you should not be experiencing the problems you have described.
Please visit the support page for any FAQ's that may resolve this situation, and thank you for bringing the matter to our attention.
Thank you for contacting the SQUARE ENIX Support Center. For additional assistance with this issue, you can reply to this email directly. For assistance with a new issue, please visit the SQUARE ENIX Support Center at
http://support.na.square-enix.com.
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Perhaps If there are more reports they will realise that there is indeed a problem.
Now , if instead of this crap game center stuff, all the apps would support using the itunes file sharing options , one could save the game user data on the mac then restore them later on on the device. Because it is nice to say you can reinstall but (because the iOS is so limited about that) this means lossing all your data each time you uninstall an app.