Unfortunately, we have been unable to reproduce this behaviour ourselves. When we tested some Leanpub books in the Kindle app on iOS devices, the place was always preserved.

Since we've unable to reproduce it, unfortunately there's little we can do to help. However, in case you are unaware of it, Kindle does have a bookmark feature - if you tap the top right of a page, you should see a little bookmark appear, and this should help you navigate back to where you were, when you next open the book.