The app failed to download/update from the App Store

The installation of apps is fully under iOS control, and when there are problems, they are on the App Store or iOS side. There is absolutely no way for apps to influence the installation process.

If the app installation fails, the best thing to try is to delete it and install it again from the App Store (and possibly restart the device beforehand). You don't have to worry about the payment — the App Store remembers that you have already purchased it, so you won't pay twice. You might also search the Internet to see if other users are experiencing the same problem — the App Store could be temporarily down, there may be some issue with the particular iOS version you are using, etc.