Hello David,
The latest app requires iOS 6 or later, Apple discontinued support for older devices, not us. Apple does not do well with backwards compatibility and changed a lot in iOS 6 breaking functionality in prior iOS versions. It is very unfortunate, Microsoft does a great job with supporting prior versions, Apple assumes everyone will update to the latest or buy new devices more frequently. We considered an update to try and support older iOS versions but at this time it is not a priority as most have updated to iOS 6 and we need to keep our efforts focused on the new APDL app for iOS. You can continue to use the 3.5.1 app you should have installed and is a solid app with no known issues. If you are getting an update notification from Logbook Pro then you can turn off the update notifications in the Settings area of the app.