Let's say William is performing worse and worse in his tests/exams recently, how do you describe this situation? Is it natural to use the word 'regress'?
William is regressing in his studies.
Just as you put in your description, I would use either getting worse or not improving. If you're looking for a single word, it would probably be failing:
William, your grades are getting worse....
William, your grades are not improving...
William, you are failing.
These are only a few suggestions. There are many ways to say this.
It sounds as though his work is deteriorating. See https://www.dictionary.com/browse/deteriorate