So, I've seen similar threads but nothing regarding this exact problem. I backed up to iTunes last night but with iOS9 no apps are transferred to the computer. When I restored it looked like everything was going great but then it just stopped downloading apps to get everything back. Now the only way I can get apps to download is to go search the app store and press the cloud redownload button. My wife had the same problem and hers seemed to be downloading the apps with this workaround but then she tried to use one and it seems it's not on her phone after all? Tried multiple restarts and signing out/in to the App Store, complete with billing verification.