Town were the better side against their promotion-chasing opponents and created the much clearer chances, but have now gone six hours without a goal, a run that simply has to end soon.
How it didn’t here remains a mystery as Halifax forged some extremely presentable opportunities as they huffed and puffed but were ultimately left to rue some poor finishing and decision-making in front of goal.
Jordan Burrow prodded wide at the near post from Josh Macdonald’s cross, then headed straight at keeper Ross Flitney from Nicky Wroe’s cross six yards out.
A superb run by Richard Peniket carved out a chance just after the restart, but Burrow’s poke went wide.
Peniket himself then spurned the best chance as he charged to the far post unmarked to reach a cross but chose to cut the ball back rather than shoot.
James Bolton’s looping header was acrobatically tipped over by Flitney before Eastleigh scrambled the ball off the line from the resulting corner.
Halifax: Johnson, Hibbs, Bolton, Roberts, McManus, James, Wroe, J Macdonald (Hattersley 79), Peniket (Fairhurst 74), S McDonald (Hughes 66), Burrow. Unused substitutes: Porter, Harrison.
Eastleigh: Flitney, Partington, Green, Drury, Coulson (Cook 74), Turley, Evans, Odubade (Midson 60), Reason, Strevens, Tubbs. Unused substitutes: Poke, Reid, Harding.
Referee: S Bennett (Staffordshire)