I've noticed this behavior in both a single WP & WPMU setup where WP is a default setup and WPMU installed with your Membership plugin.
Simple WP: user who logged in before the Support System plugin was installed won't see the Support menu in the dashboard nor have access to it via manual link. Hence, no permission.
WPMU with Member: Support system available for Level1 (subscriber) and above. Visitor (guest level) signs up as Level 1 (subscriber), can see Support. Upgrades to Level 2 or whatever, still can see Support as supposed to. But if downgrading back to Level 1 (subscriber), Support is gone (same as in simple WP setup).
From my gut's feeling: there's something with the permissions. Yes, no matter what I set in the Support System settings' permissions, it won't make a change.
Something I wasn't able to test thoroughly was "what if the user was already on a permission level that the Support System settings would allow anyway"? Means I did have the users created before the Support installation on subscription level and initially Support was set to not accept Subscribers. But then I both switched those users to a higher level and I allowed everyone in Support settings to access it. Yet it fails for those specific accounts.
Is there anywhere an option saved in the database that I missed? I compared users with and without access to Support System and the Support System's own entries but couldn't find anything hinting into the right direction.