what makes a cheese sauce break ?

The proteins break down from getting too hot which makes it curdle. It is a mix of fat, protein and water and the protein connects to both of them. Using a skim milk instead of a whole milk will also make a sauce break since the fat and water have to be balanced.

Make your white sauce, remove from the heat, cool for 5 minutes in the pan, and stir in cold cheese until it melts.

Continuing to cook the sauce after adding the cheese makes the sauce break, making a greasy gooey mess.

Normally the cause is too much oil or fat in the sauce. Don't forget your cheese could be releasing more fat. For example, cheddar has more fat in it than Velveeta or American cheese.

Another cause could be heating it to a boil after you've added the cheese.

if u add prepackaged grated cheese instead of grating a block it could curdle as the pre-grated stuff is coated in flour and doesn't mix in as smoothly.

Over heating it, do not let it boil! If it does break sometimes you can save it by putting in a blender. Good luck!

Adding too much liquid at once without slowly emulsifying it properly first

Flour, like in a fondue.

Could you please add more to your question?