No one expects the mods to make perfectly fair decisions. I can understand the mods being more patient to those they know more, those who have been here more, those who are more reputed but here we are talking about Burke. The way you treat him differently than the other members doesn't suggest small imperfections Swag. The mod team has been patient to his behavior SO much that all the members have learned not to complain about his behavior to you.
Mods are not above criticism, however. The constructive stuff is good. I like it when people approach me when they feel they are being unfairly handled by another mod. Most of the times I disagree with them.

But sometimes I agree.
As you say, however, this may have lead some members to no longer bother raising it.
The reason why some "unpopular" members are more often subject to rule enforcement than the "popular" ones entirely has to do with how the most effective mods should almost be completely anonymous. If you're anonymous, context is hard to interpret differently because you have no history with the person. And when you have no history with the person, chances are that you're not likely going to have a friendly chat with them in some other thread a few days/weeks later that might otherwise be made a little awkward with a previous ban decision.
While I don't issue many cards much these days compared to the other mods (part of that due to time on the site lately), oddly my cards are typically issued to regular members I know and not "unpopular" or new members (save for the spammers

).