Why is it that sometimes the shells of hard-boiled eggs don't peel very easily?

Understanding the anatomy of an egg will give you a clue. Eggs have a thin membrane attached to the inside of the shell. The fresher the egg the tighter the membrane is attached to the shell. This membrane shrinks over time so that a boiled egg becomes much easier to peel. I try to always have at least a dozen eggs that have passed their expiration date on hand, these are the ones I use for deviled eggs. This is one time where fresher isn't necessarily better.

http://www.edinformatics.com/math_science/science_...

I notice after the egg has cooled down a bit(I put my eggs in cool water) they are easier to peel. I've also noticed if I wet my hands a little and start to peel the egg, the shell comes off a little. easier.

The fresher they are, the harder they are to peel.