Jonathan... You've asked a good question.
There is no rule to follow.
The most important consideration is whether the two actions, i.e., surrender and retreat, are the same actions or if they are different actions.
In this case they are different, so it would be best to use 'no' in front of each of the two actions.
In the example "I didn't lie and cheat", lying and cheating are different actions, so it is better to say "I did not A and I did not B."
It isn't absolutely necessary to repeat the negative "no or not", because most people will realize that you mean that you did not do A or B. But it is completely clear to the reader to say that each separate, different action was not done.
I hope this helps...