The gamble to put the club into administration just over a couple of weeks ago is starting to look far riskier than anyone had imagined.
And this latest setback took their recent bad run to four successive league defeats, during which they have failed to score a goal.
The positive to emerge from the game in Devon was that a patched up side battled to the bitter end and with a little more luck might have snatched a point in the final minute.
But it was a familiar story in Devon with Town having the chances to get something from the game, but being unable to find a way through.
And Exeter took the points when Richard Logan bundled the ball home from close range on the hour.
Town had started brightly with Anthony Griffith, playing at right back in the absence of Gareth Davies, setting off on a second minute run before cutting inside and curling a left foot shot narrowly wide of the far post.
Craig Mawson looked confident in goal as he came out to punch clear from a Wayne Carlisle free kick and a Dean Moxey corner and there were fine defensive interventions from Santos Gaia, from a Ryan Harley cross, and Tom Kearney, who headed clear from Carlisle.
The first indication that things were going against the Shaymen came after 19 minutes when Matt Doughty was booked for a dive when he had clearly been fouled - inside his own half - by Matthew Gill.
But they had their best spell of a low-key first half after that with a Gaia free kick looping up off Jon Shaw for Simon Heslop to volley over the top from the edge of the area.
Moments later, Rob Edwards conceded a corner which was swung in by Doughty, but Gaia, back at his first English club, headed narrowly over the top.
Doughty cleared a Moxey corner, Logan sent a glancing header well wide and then missed from six yards with the home side's best chance of the opening period.
Town were handed a warning about the threat of Gill's long throws within three minutes of the restart when he sent one in from the left that ended with Logan heading wide again.
Shaw responded at the other end with a headed effort from a Daryl Taylor cross after the sub had done well on the right, but the striker glanced the ball wide.
Logan had a chance to break the deadlock in the 58th minute when he raced clear, but Mawson was quickly off his line and the City striker snatched at his shot and fired wide.
Two minutes later, from much closer range, Logan broke the deadlock when he was on the end of Matt Taylor's flick from a Gill long throw.
Harley's quickly-taken free kick almost caught Town napping, but Gill's shot from the left was saved by Mawson at his near post.
Town responded with Shaw finding Taylor on the left, but his shot was straight at Andy Marriott.
And Kearney's right wing corner in the 71st minute picked out Lewis Killeen who controlled well and hit a decent shot, but Gill blocked.
Moxey fired wide from distance and Harley saw an effort deflected over the top as Exeter looked for a second goal.
But while there was only one goal in it the Shaymen always had a chance of salvaging something from the game and they almost did it in the final minute.
After being helped down the field by a couple of free kicks, the ball was floated beautifully to the far post by Heslop where Gaia did everything right.
He got power on a downward header and for a split second it looked like an equaliser, but Marriott dropped to the floor and kept it out to dash Town's hopes.

MATCH FACTS
Exeter City: Marriott, Sercombe, Matthew Taylor, Seaborne, Edwards, Carlisle, Harley, Gill, Moxey, Logan (Watson 79), Stansfield (Basham 79). Subs (not used): Jones, Friend, Cozic.
Booked: None
Sent-off: None
Goal: Logan 60.

Halifax Town: Mawson, Griffith, Wright, Gaia, Ainge, Doughty (Harban 69), Killeen, Heslop, Kearney (Whitehouse 81), Shaw, Forrest (Taylor 46). Subs (not used): Legzdins, Atherton.
Booked: Doughty, Mawson.
Sent-off: None
Goals: None

Attendance: 3,096
Referee: S Hooper (Swindon).

STAR SHAYMAN
With the wind blowing and the rain sweeping the length of the St James's Park pitch it was always going to be an afternoon for keeping your concentration.
And, one first half slip apart, Jake Wright did just that in the heart of the Town defence.
He barely missed a header all afternoon and his distribution was generally good when in possession.
Anthony Griffith showed his versatility with a good display at right back from the kick off.
He was never troubled by the dangerous Dean Moxey and broke well to cause the home defence problems.
He then reverted to a more familiar midfield role late on as Town looked, ultimately in vain, to get back on level terms.
Craig Mawson kept his place in goal and justified the faith shown in him by Chris Wilder with a confident display.
He punched clear on several occasions, handled well in tricky conditions but was left exposed for Richard Logan's goal.
Wright takes the three points on offer in our season-long competition with Griffith claiming two and Mawson one.

PLAYER POINTS
Jon Shaw 43, Simon Heslop 39, Anthony Griffith 24, Andy Campbell 22, Tom Kearney 21, Jake Wright 20, Lewis Killeen 14, Matt Doughty 12, Steve Torpey 12, Steve Bushell 10, Danny Forrest 13, Daryl Taylor 8, Rob Scott 7, Tom Clarke 6, Adam Legzdins 6, Cortez Belle 5, Craig Nelthorpe 4, Craig Mawson 4, Adam Quinn 3, Peter Atherton 2, Nathan Joynes 2, Darryn Stamp 2, Ryan Toulson 2, Greg Young 2, Simon Ainge 1, Gareth Davies 1, Santos Gaia 1.

YOU SAY
Same old story away from home.Get rid of Wilder and put Frode Grodas in charge til the end of the season - Angry Anderson.

Is there a 'White Knight', with 'no sense' out there. B'cause Mr Wilder has expunged his full reservior of excuses - burtonblue

Other clubs battle and get results whist soft town travel 300 miles to defend. Wilder out now - para farrar

Nice of the players to acknowledge the fans whilst wilder ignored us and sulked off - ronnie warren

Mawson, harban, kearney & taylor all play, & we still lose! I just can't understand it - sarcastic town fan

A typically inept defensive away performance, any wonder we are doomed - angry andy