I have no idea what's the reason for this behavior.
ADDED. This flair page shows the default math.SE and the combined SE flairs, but not the clean, dark and hot dog stand math.SE flairs.
ADDED 2. I've just seen that all my MSE flairs now show properly, but the flair page mentioned in my last edit remains unchanged.
ADDED 3. This bug is MSO Flair 500 Error, as pointed out by Martin Sleziak, and has already been fixed and tagged (status-completed) there. Apparently, now it is fixed here too.