I'm having a similar issue. I have the latest iTunes for Windows installed and it shows about 15 App updates available. When I click "Update All" it appears that it communicates with the App Store and then nothing. No error, no downloads, no nothing. I've verified that iTunes can connect to the App Store as I've logged out of my account and back in again several times. I've also used the iTunes Diagnostics to confirm connectivity.
I have an iPhone 5 and an iPad Air 2, both iOS 9, and both have downloaded all app updates but when I sync either with iTunes it still shows all the app updates as needing to be downloaded.
I've tried rebooting the devices and my laptop several times and have even uninstalled and reinstalled iTunes. All without success. Any help is appreciated.