Béarnaise, Hollandaise, mousseline etc. can turn out too thick even when making it and certainly when it cools down.
THE trick to loosen it again is to add a tbsp of very hot water. Plain and simple.
These sauces are never served hot, always luke warm.
A good dosage may prevent left-overs; I mostly make Hollandaise for 2 or 3 people and it's mostly gone. I use 2 eggyolks, 2 tbsp of water and a very small dash of lemonjuice (about 1 teaspoon), start whisking on the smallest fire and remove the pot frequently from the fire. It takes around 5 minutes of vigourous beating to get to the next stage.
When doubled in volume and no liquid left over at the bottom of the pan, add small cubes of fresh butter, a few at a time and keep stirring until dissolved. I guess I use no more than 50 grams of butter (in fact; to taste)!!! Taste for seasoning; add more lemonjuice if needed and s& white pepper.
Using clarified butter is old skool; raw butter gives a nicer taste much faster so you don't need an excess of butter to make Hollandaise or similar sauces. You don't need to believe me, just try it.