The argument worth continuing should still be producing understanding rather than merely new sentences.

Some arguments stop moving long before they stop happening. Words keep coming, positions get restated with different emphasis, and nobody learns anything after the first twenty minutes. The test is not whether it feels important, since it always does, but whether either person is ending up somewhere they had not been at the start. Motion is not the same as progress.

Mid-disagreement, ask yourself what you have understood in the last few minutes. If the answer is nothing, say so plainly and suggest coming back tomorrow. Pausing is not conceding, and it protects what you will need afterwards.