Consider trying to download the Mac OS X 10.6.8 Update Combo v1.1 instead of using Software Update. You can also give this a try to fix SU:
Fix for Software Update
Delete the following files:
- /Home/Library/Preferences/ByHost/com.apple.SoftwareUpdate.xxx.plist where "xxx" is a number.
- /Home/Library/Caches/com.apple.SoftwareUpdate/ (delete entire folder)
This reply may seem late but might as well share my findings.
I have the same problems with the software updater for 10.6.8 as well after trying to move on to Mavericks from
OS X Leopard 10.6.8.
Tried the patch as well the listed files to delete and etc but all failed.
Then I noticed the problem was with the software updater complaining that there was a network problem and even though the dignostics was run the results were no network connection exists but Air Port is connected and there is no issue browsing the web.
I took a look at the Wi-Fi settings and noticed that the default locations were going back to an old Wi-Fi network location I had latched on to 4 years ago! I assumed some screw up with the Wi-Fi network software and thus removed all Wi-Fi network associations and locations and reconfigured the Wi-Fi from scratch for my local home Wi-Fi network. After this the software update worked fine and can now download updates. Note that I did install the update patch by Apple though in my first attempt to resolve the problem.
I would consider the possibility of the Wi-Fi software services within OS X Snow Leopard being a bit "buggy".
Deleting all the non used Wi-Fi network associations and clearing or resetting the default location settings helped revive/resolve the no network connection problem with the software updater.
Now can move on to Mavericks...