This problem has been solve yesterday. Previously, I had tried the methonds mentioned in this discussion and none can solve my case. Tried Apple Care (not much use), Apple Store Genius Bar, (not much use)....
The important thing is you have to backup your iPhone / iPad before resetting it in order to solve this problem.
(1) Backup your iPhone / iPad to iCloud. If you don't have enough storage, try to remove some less important data like photos or videos, buy more iCloud storage until it's enough. (Call back Apple within 2 weeks to ask for a refund later when the problem is solved)
(2) Reset your iPhone / iPad ... Setting > General > Reset > Erase All Content and Settings
(3) Restart iPhone / iPad as a new device, do not restore from backup at this point.
(4) When it's done, connect to iTunes and 'Backup to this comptuer', let the process finish and this means the 'disconnected' problem is solved.
(5) Unplug iTunes, use iPhone / iPad connect to iCloud and restore from the lastest backup file. This will take hours depend on how many GB is the backup file.
(6) At this point, your iPhone / iPad will be the same before resetting. Connect to iTunes and 'Backup to this computer'. It is then back to normal again. Good Luck.
If you think paying money to increase iCloud storage and then ask for a refund is stupid. Try to creat a new user in your computer (both apply to Mac & PC), connect iPhone / iPad to iTunes and try to backup. Remeber to Authorized & Deauthoried your Apple ID to iTunes, then reset, then restore.
This 'disconnected' problem may be casued by some corrupted files inside your iOS device, but it's not easy for us to find out which APP causes the problem. So, we are here in this discussion.
Hope this can help.