A deadlock in which neither side is able to defeat the other is called a?

I would say that in a military sense it is called a 'stand off' and that it is when both sides are in a stalemate with neither side able to claim a victory. This happened in the 1990 Oka Crisis in Canada when the First Nations Mohawk people occupied a golf course that belonged rightfully to them but was stolen from them and never returned so at first there was a stand-off between the Canadian military and the First Nations warriors. So in conclusion, stalemate is the better term for this situation.

A war of attrition.

World War 1 is an example of this.