You could try accessing the workshop from within Steam itself, rather than a regular browser. That should avoid the need to log in.
I assumed he was doing this....
There's a bug in Steam that makes you have to log on manually even in the Steam browser.
Usually restarting Steam fixes this but on some systems it seems this ALWAYS happens (not sure of the cause)
I do believe every time you login on an actual web browser you have to verify with Steam guard each time though...
Or at least most of the time.