Looking for backup disk...

So you did a clean install of Mountain Lion??

How often the problem happen? It is apparently successful sometimes and failing at other times.

Freezing finder shoud not require a reboot of the Mac.. just a restart of finder. But I am not running ML so perhaps that is a different issue.

Are you using SMB names for the everything in the TC including the hard disk.. ie short, no spaces. pure alphanumeric?

Could you test the problem another way by using a USB drive as a target for TM and see if that works ok?

Install the widget.

A1 http://pondini.org/TM/Troubleshooting.html

You need as much info about what is happening as possible.

The disk not available problem is also there.

C9 and C10.

Definitely you need to use 5.6 airport utility.. so you can actually get into the logs of the TC.. v6 utility has no access to the TC logs. strange that.

How to load 5.6 into ML.

1. Download 5.6 for Lion.

http://support.apple.com/kb/DL1482

Click to open the dmg but do not attempt to install the pkg.. it won't work anyway.

2. Download and install unpkg.

http://www.timdoug.com/unpkg/

Run unpkg on the desktop.. it is very simple.. drag the AirPortUtility56.pkg file over to unpkg.. and it will create a new directory of the same name on the desktop.. drill down.. applications utilities .. there lo and behold is Airport utility 5.6 .. drag it to your main utilities directory or just run it from current location.

You cannot uninstall 6.1 so don't try.. and you cannot or should not run them both at the same time.. so just ignore the toyland version.. the plastic hammer.. and start using 5.6.. a real tool.

Copy and paste the log from the TC when you have the issue..

How old is the TC? And how old is the computer? You might have an actual hardware fault.

Ethernet on the TC can slowly go bad.. Gen 3 in particular I have found to have this problem.

Do you have both wireless and ethernet running? I would turn wireless off.. to ensure just ethernet is working.. or visa versa.. do not mix both methods of connection.

Please open terminal and ping the TC.

You said you had changed to SMB names.. but the widget log shows you are using names that include apostrophe and spaces. Particularly the hard disk name should not have spaces. I cannot see its name.

I particularly recommend you do TM backup to USB drive directly plugged into the computer.

After that I would go back to factory settings on the TC.. redo the setup with smb names. Erase the hard drive and start again.. You need the log from the TC .. not just TM..

I never said anything about changing to SMB names. I left everything as it was before and working for more than 1 year. All of the sudden, without any change, except maybe some updates, it could not be accessed for automatic backups.

I listed a number of things to try.. you said..

Unfortunately, I read these before and tried them and they could not help me.

I took that to include the suggestions.. that included SMB names.. I do know many people have reported issues with using a split name on the hard disk.. and Apple used different default names on different versions of the TC.. for reasons I do not at all follow.. but I think if you are trying to track down an issue.. then using all possible means available is necessary.

The updates have caused issues.. if you check the Mountain Lion area.. there are issues with TC and TM.

I can only recommend you try each of those things.

I do think the log from the TC will help as there are issues with AFP dropping out.