I've got three 10.6 computers that won't install OS X updates. Checking for new software will show about a dozen updates (Security updates, Safari, iPhoto, printers, etc) and if choose install it downloads them. After downloading and then clicking restart the computer sits at the purplish sky desktop with no progress bar, and then after about 3 minutes it goes back to the login window (without ever installing or restarting).

If I then select check for updates the same updates will all be presented and I can repeat the process. Manually downloading and installing an update such as 10.6.8 combo updater works as it should, and then check for updates no longer presents that particular update as an option.

This seems to be the result of some setting or 3rd party application as I've got 3 out 7 computers experiencing this exact same problem. What could cause this and how can I fix it?