Button to allow ADB backup not working
For me force stopping the Facebook Messenger seemed to fix the problem.
In your case it might be related to a different app.

Go to Settings->Apps->Select the application you suspect->Press "FORCE STOP"

Possibly this is related to the "draw over other apps" privilege.

Also see http://forums.androidcentral.com/htc-one-s/520618-adb-backup-can-t-click-back-up-my-data-button-phone.html