Do these apps actually conect to the internet without problems? Do you get notifications for default apps like Messaging and wifi?
Do you use Stamina mode? Then try excluding these apps from Stamina mode. If that doesn't work, try clearing cache or data of these apps, or try uninstalling and then reinstalling these apps.
Settings--Apps--All--choose the app--Clear cache. Reboot.
If it doesn't work, try this: Settings--Apps--All--choose the app--Clear data. Warning: This will delete all preferences for the apps including all data stored within the apps like accounts, bookmarks, favourites, etc. The apps will become as clean as they were when you installed them first. Reboot.
If nothing works, try a repair of your phone using Sony Update Service.
