Robin shouldn't have been given the job in the first place, so I don't care if he gets fired. That being said, this is a bad team and the record reflects that. I'll never get myself into a debate about how much a manager is responsible for a team's record. But at the very least, I don't believe there is any good evidence that tells us that going against convention here (hiring a guy who's coached at AAA and worked his way up for, etc) is a smart move. As far as I know, Robin was not even the head coach of a high school team before he took the Sox job. And it's not hard to see where his inexperience has led to undesirable results.
The way this organization has done things the past 10 years or so, it would be shocking to see him fired before season's end. Given his personality and the way he does his job, there'd have to be a pretty dramatic Ozzie-like shift in how he handles things moving forward to be canned.