IPhone – Unable to install app on new phone because “App is no longer available in the App Store”

When you purchase apps (even free) on the device, iTunes always backs this up - and when it Syncs, before it does anything it backs up - and it notices that you have purchased an app/apps - so it wishes to make a backup of these apps. Click transfer and it'll all work fine - happens to me when I buy songs off of the store as well as apps

Firstly, you must bear in mind that each In-App Purchase is uniquely associated with an Apple ID and that there are different In-App Purchase types:

• Consumable - You need to purchase these items every time you want them, and you can't download them again for free.
• Non-Consumable - You purchase these items one time, and you can transfer them to multiple devices authorized with the same iTunes Store account.
• Non-renewing Subscriptions - You can purchase these items again after the subscription period ends.
• Auto-Renewable Subscriptions - You can purchase these items with different renewal periods.

There are, therefore, differences in the way the availability of the product is handled.

As stated on Apple's iTunes Store: About In-App Purchases:

You can't sync or transfer non-renewing subscriptions and consumable In-App Purchase to another iOS device or Mac. You can transfer non-consumable In-App Purchases and auto-renewable subscriptions to another iOS device or Mac authorized with your iTunes Store account. For example, if you transfer a game from an iPhone to an iPod touch, only the game levels will sync, and the extra ammo and experience points won't transfer.