And if ever there was a time they needed to end their long barren run at the Devon ground, it is now.
Not since May 1988, when they won 2-1, Peter Duffield and Lee Richardson were on target, have the Shaymen earned a winning bonus away to the Grecians.
And draws are reasonably scarce as well, the last coming in August 2003 when the opening game of the season ended 1-1.
Each of the last three trips to St James's have ended in defeat with the Shaymen having conceded eight goals.
Having gone into Monday's game at Droylsden as strong favourites - and lost - the Shaymen will be massive underdogs tomorrow.
But there is pressure on the Grecians after their charge towards the play-offs stalled when they were beaten at Weymouth in their Bank Holiday clash.
The key for Halifax tomorrow could well to be keep the scoreline goalless for as long as possible in a bid to create an atmosphere of frustration.
The defeat was Exeter's second in successive away games, having lost at York City a fortnight earlier.
But their home form has been good all season and they have won seven of their last eight games at St James's Park, the only blemish being a 2-2 draw with Woking when the Cards came back from two goals down at the break.
That helped them to the top of the form table in February, although things are not going quite so well this month.
Exeter have been a fairly ruthless side this season having won 15 of the 25 games in which they have taken the lead and when they lead at the break, they do not lose.
They have also won nine of the 11 games in which they have kept a clean sheet so the Shaymen will almost certainly have to score if they are to get any reward.
Chris Wilder's side will travel in hope rather than expectation and anything they get will be a real bonus in their continuing battle to beat the drop.