I don't know of a specific time limit.. I try when I can to put iodine on them but try to feel it and see how it feels. If its dried up some I wouldn't think its infected.
I agree with what has already been said, and would add that if there were a problem in addition to being swollen the calf would be laying around a lot and probably kicking some when standing up.
Unless it's swollen and oozing and feels hot to the touch, I wouldn't worry about. I've seen some still have some remnant of the cord 3 to 4 weeks after birth. It will come off eventually.