As raised on mailing list: "[Android] Apps restart instead of resume when brought to focus by clicking app icon"
"TLDR; AndroidManifest.xml <activity> needs: android:launchMode="singleTop" – can I add it?
..which advises to add android:launchMode="singleTask" to AndroidManifest.xml <activity>, which does fix the issue.
According to the descriptions in http://developer.android.com/guide/topics/manifest/activity-element.html the differences mostly stem in how the app handles intents, however, there is a comment in the table of descriptions which labels singleTask launchMode as "(not recommended for general use)".
On the other hand, singleTop mode is recommended, and also fixes the issue, and according to the description, sounds to me like a much better default."