Umbilical cord question?

My son is 6 weeks and his cord stump is still there, it is still pretty firmly attached. I had him at the DR for his 4 week check up and the DR said to keep alcohol on it and it would fall off in time. It doesn't look infected, isn;t red or anything, it just won't fall off. I have 3 kids and have never heard of this happening. Anyone else experienced this? Is this something to be concerned about?