I had the same problem today.
In the Apple Developer website, all of my company's Provisioning Profiles were marked as "Invalid (managed in Xcode)". None were out of them were date, none were using iOS Certificates which had expired, and the website gave zero suggestion that anything was actually wrong.
The solution, ridiculously, was to delete my perfectly valid iOS Certificates, and recreate them.
We write in-house apps aswell as apps for the App Store, and Apple (quietly) refuses to let you have more than 2 of these at once. So I was unable to create a third iOS Certificate which would allow me to use the "In house and Ad-hoc" option, hence the need to delete an iOS Certificate first.
Once I had pointlessly recreated the "iOS Certificate", the Provisioning Profiles came to life.
Part 2 of this farce is to go into Xcode, and delete your Provision Profiles (XCode \ Preferences \ select your iOS Certificate \ View Details, then select all of your provisioning profiles, right click and select "Move to trash".
At this point, absolutely nothing will change, and you'll think you've done something wrong.
But then, if you then quit Xcode, and go back in, then you'll see the Provisioning Profiles will have disappeared.
Now you can re-download the Provisioning Profiles from the Apple Developers website, and redownload the latest versions.
Until Xcode 7.2 comes along, and breaks something else.
(Seriously, I spend more time fighting with Xcode bugs than writing code..)