Gillingham hit the woodwork twice while Stanley had an effort cleared off the line as it was goalless at the Priestfield Stadium.
Jonny Maxted was the busier keeper, making some vital saves while the post and crossbar saved the Reds as well.
But Billy Kee was desperately unlucky to have his effort cleared off the line as Stanley are still hunting for their first League One win in 2019.
Midfielder Scott Brown came in to replace the suspended Dan Barlaser but it was the Reds who had to defend early on in rain-swept Kent.
The first real chance fell to Darren Oldaker on 17 minutes with Maxted having to palm his effort around the post.
Stanley had to soak up some pressure and a dangerous low shot across the goal from Tom Eaves clipped the far post and thankfully for Stanley bounced out for a goalkick.
Maxted denied Elliott List while the Reds began to get more into it towards the end of the half.
Kee headed off-target with one chance and the striker then chested down for Jordan Clark in the area but his acrobatic kick was over.
On the stroke of half-time Maxted had to punch a List effort away as neither side could find a way through.
Stanley started the second half well with Brown firing wide from distance but Maxted was again soon in action, denying former AFC Wimbledon captain Barry Fuller.
Gills keeper Tomas Holy made routine saves from Clark and Sean McConville while Maxted kept out an Eaves strike as the game went from end-to-end.
Clark played in a great ball for Ross Sykes but the towering defender couldn't get enough power on his header and Stanley were desperately unlucky on the hour mark.
Kee got his head to McConville's free kick but Eaves was there to clear the ball off the line.
However it remained in the balance with Maxted keeping out Max Ehmer and the Gills hit the woodwork for the second time on 67 minutes.
Oldaker's free kick was tipped onto the crossbar by the Stanley keeper as Maxted kept Stanley in it.
QPR loan signing Paul Smyth came on but it was captain Seamus Conneely who had the next chance, volleying wide of the post.
Maxted was alert to stop Josh Rees having a clean shot on goal with eight minutes remaining as neither side could break the deadlock.