MORE Push Notifications
I lost everything after going to farm a fort that was 45mins away by cat.
Since I'm not on the app 24/7 I closed it, and went to do something else. Usually I set a countdown alarm on my iPhone, but on this rare occasion it was late (1am!) and so didn't want to set an alarm. I resolved to remember it.
I forgot.
Now, a push notification which states "Lord Phil! Your troops approach the enemy!" 2 minutes before battle would have saved my cats.
My beautiful, beautiful cats.
Also, notifications for things such as "low crops! feed the men!" and "Full resources, upgrade your warehouse!" would help novice players get into the game, without having to learn by the frustration of losing half their men to starvation.
For a 24/7 connected game, it does little to engage a player who isn't sitting and staring at the screen all day/night.
My cats

Alliance : Monti
Server13
Alliance : Demented