App updates, downloads, and in-app purchases are all handled through Apple iTunes Store. If you are having problems, confirm that you are using the correct iTunes Store Apple ID account, and use Apple’s support web site for diagnosis.
Open the Settings app on your device, select Store, and inspect your Apple ID. Then, open iTunes on your computer, select iTunes Store, then Account, and confirm that it matches the account used on your device. Then select Purchase History and locate your purchase, to confirm that it is the same account used to make the purchase.
Go to http://www.apple.com/support/itunes/, Apple’s support web page, to see if your issue is described there. Alternatively, use a search engine to find support web sites that may also describe the problem and possible solutions.
If you find an Apple support page that matches your issue, but you still cannot resolve it, use the EMail Us link on that page to contact Apple directly for further assistance.