It's a huge bug bear of mine at ours should HID and myself get the chance to go out in the week together. If I can't get us a tee time before 10.00am I know that we will be held up by a group of 4 men and not let through 99% of the time and I can tell that before we've even finished the second hole.
If it’s the same 4 every week, ask them why they won’t let you through. And ask them the next time too. If you don’t want the confrontation, ask the Captain to have a quiet, unofficial word.