If it happens so that the game is crashing on your iOS device shortly after the launch, you need to do the following:
1. Navigate to Settings -> Notifications -> On
2. A list of apps that support push notifications will appear. Make sure that notifications for King's Bounty: Legions are turned on (see the picture below).
3. Reinstall King's Bounty: Legions.
These actions are supposed to solve the problem.