I just tried this in the historical battle where old cold harbor was listed as contested when the mission timer hit 0. The battle continued until contested hit 0 and resulted in a victory. The draw was because you didn't take less than 40% casualties in your initial force. The victory conditions apparently only consider forces on the field rather than total army size committed. 8750 deployed, 3864 casualties. I was able to reproduce a draw under the same conditions when I took enough casualties.
If you haven't captured old cold harbor, still control the central breastworks, and haven't taken too many casualties when the timer hits 0 the battle should move to the left flank. Assuming you don't capture victory points early and don't take too many loses the battle should keep switching between the left and right flank and extend to 3 days.