How to prevent/slow down fava beans from turning to darker color?

I think the answer lies in how you're cooling them (hence my earlier comment). Many vegetables need to be 'shocked' immediately after cooking in order to retain a vibrant color. As shocking stops the cooking process, it also contributes to maintaining a good texture and flavor.

Here is a very similar Q & A from The Globe and Mail:

The question: I love fava and green beans in the summertime and would love to serve them at dinner parties, but they always look dull and grey after I cook them. Whenever I have them in French restaurants, they're bright green and vibrant. My daughter insists the chefs are probably just using MSG. Is she right?

The answer: It's not likely MSG they're using - just a simple technique called a "big pot blanch and shock." The key is to cook your green vegetables as quickly as possible so the heat doesn't have time to release their pigment and then shock them in ice water as soon as they're done. Fill the biggest pot in your kitchen - I use an eight-litre stockpot - with cold water and bring it to the hottest boil your stove can muster. Add a cup of table salt for every four litres of water, then dump in only as many vegetables as you can add without stopping the boil. Cook them in batches if you must. When they're done, scoop them out and chill immediately in a big pot of ice water. And maybe wear some protective sunglasses. They're going to be that bright.

Since, at the end of your cooking, the beans have the nice color and flavor you like, I would suggest cooking as you normally do but use the shocking technique immediately after.

If you normally keep the beans in the cooking liquid, I would still shock the beans and refrigerate them separately from the liquid. You can refrigerate the liquid and, when cold, add the beans back in.

Your observation is interesting in that fava beans contain high levels of oxidants. Persons with genetic susceptibility can get very sick from eating them. This illness is called favism.

https://www.hematology.org/Thehematologist/Diffusion/8304.aspx

The problem is that the bean’s protein content can include as much as 2 percent vicine and convicine, which are converted in the gut to divicine and isouramil. These highly redox proteins are likely to retard rotting of the bean, but produce reactive oxygen species (ROS) including the superoxide anion and hydrogen peroxide, which rapidly oxidize NADPH and glutathione. These molecules are normally detoxified by catalase and glutathione peroxidase, in enzymatic reactions that depend on NADPH. Because NADPH levels are very low in G6PD-deficient red cells, these undergo severe oxidative damage. A characteristic feature of favism is that intracellular and extracellular hemolysis coexist.

Let us assume that color and flavor change described is due to these oxidants acting on the bean. How to prevent? I can think of one of 2 ways. 1: add antioxidants 2: prevent exposure to air.

The antioxidant that comes to mind would be lemon juice. The experiment is easy: a batch of fava beans, then treat half with lemon juice and the other leave alone. Does lemon juice prevent the color change? Lemon juice works to prevent browning of sliced apples by this mechanism.

The other method would be to exclude air. One could do this by tossing the fresh cooked beans with olive oil, which should produce an air barrier on each bean. Submerging beans in oil would be a surer way to achieve the same purpose. A third method would be to contain them in an airtight bag or container and exclude air first before sealing. Again, testable.

*Note that submerging cooked beans in oil is not a way to keep them indefinitely. Different and possibly more dangerous types of spoilage can happen. Both of the above ideas are to keep your beans good for a couple of days at most. Both sound delicious to me.

Use lemon skin or a bit of lemon juice while cooking. This tip is known in the fava beans restaurants in the middle east