The current version of Gospel Library for iOS supports back through iOS 6, which runs on devices that are 7 years old (iPhone 3GS). LDS Tools (the update that was just released 2 days ago) supports back through iOS 8, which runs on devices that are 5 years old (iPhone 4s). That puts the range at 5–7 years of support for a given version of an app. (The most important apps, like Gospel Library, are at the longer edge of that range.) Looking at a few popular apps on the app store (Facebook, Dropbox, Gmail), it looks like 5 years is on par with the industry standard, and 7 years is pretty good.
The Church does make an effort to extend support for the most important apps – especially Gospel Library – since they want to support members around the world, and even where newer devices are easily available, members tend to be more frugal than the general population. However, the farther back is supported, the more fallback/workaround code is required to make it work.
Developers and product managers also pay attention to market adoption of OS versions, as they make decisions on whether or not to drop support for an older operating system. For example, according to this site
, less than 2.5% of iOS users are using iOS 6 or below. With another iOS/device release for Apple just a few days away, and Apple's aggressive efforts to encourage people to upgrade, I expect that number will go down further in the next couple of months.