If you say “did not let go” instead of “wouldn't let go”, what is the difference in meaning or nuance? For example, the explanation in the grammar book I have is as follows. The car won’t start. (= the car ‘refuses’ to start) Likewise, “wouldn't let go” means “refused to let go”? (that is, past tense of “won’t let go”) Or when you use “won’t” to say that somebody refuses to do something, you only use “won’t” (the present tense + “not”)?
Will refers to intended, planned, anticipated, regularly recurring, habitual, or persistent action. Those meanings can shade into each other.
would is the past tense of will and refers to intended, planned, anticipated, or regularly recurring, habitual, or persistent action in the past.
Thus, to say
He would not let go.
can refer to a past intention or firm resolve:
Yesterday, when daddy was crossing the busy street with you, you knew he would not let go of your hand.
Daddy had no intention of letting go of the young child's hand as they crossed the busy street.
Or it can refer to a past recurring or persistent action, a kind of tenacity:
The wolf kept trying to pull the deer carcass from the wolverine's fangs, but the wolverine would not let go of the deer.
Simple past, "did not let go", states the fact more simply. Letting go simply did not happen.
To say that "he would not let go of her arm" suggests that she tried more than once to get loose from his grip.