I have a 2011 Toyota Prius with the Nav System. I also just bought an iPhone 5S. I installed all the necessary software and maps onto the Garmen USA app and things seemed to be ok as it navigated me to a destination…for the first couple minutes of my drive. Then the screen went dark. The iPhone 5S appeared to be going into lock screen mode despite having Garmin USA running! I still received voice directions, but no map screen. I don't know if this is a bug with the Garmin USA app and iOS 7 or the iPhone 5S. I would love to hear from anyone else if they are having the same problem with the new iPhone 5S and Garmin USA. I'm going to contact Garmen. If I get any news from them of value, I will update this post.
P.S. I have been using this app for over a year on a iPhone 4S running iOS 6.x.x. Never had this problem. Just started with the iPhone 5S and iOS 7.