...as follows:
Sergi and Kevin are hoping to determine if the LDAP lookups are working correctly to help you troubleshoot.
After hitting the "refresh" button as directed by Kevin, the SWG should actually display a whole lot more information regarding the user, including the groups this user belongs to. What you're looking for, is to find out if the SWG is able to see the user as belonging to the group you tried to allow out, in accordance with your opening post?
If the SWG is able to correctly see this user's membership to the group, then it might be worth testing out your original policy again, or testing with a new policy applying to the target AD group.
Going back to the first post, I don't see any information about the SWG suddenly stopping a user. Can you elaborate please?