David,
I recommend you open a ticket on this. There can be some variables at play that are difficult to advise via forums. Behavior may be slightly different in 6.2 than in 6.3 just because there are some minor variations in the way credentials are used for some patch functions. I could provide some very generalized information, but a ticket will be the best route to figuring out what's occurring, why, and how to prevent the same issue from reoccurring.
From a general perspective, test whether the behavior is different when there is a user logged onto the machine v. when you run the test when no user is logged in. It's possible that the network is able to authenticate/allow the tasks when the logged on user is present but not when no user is present. This could be due to proxy, firewall rules, webfilter, or local security policies.
The patch test status is static - if failed, the notification of failure will remain until the next time the test runs. Therefore, it's quite possible that the test will fail due to some environmental issue (whether that's internet or access rights or anything else) but then pass next time because the underlying condition of the failure is no longer present.
In any case, with a ticket, we can access your system and investigate the root cause for your particular environment.