It was the hosts who started the better of the two teams, Kyle Perry’s header cleared off the line by Alex Moore.
Applying further pressure, Charlie Dowd and Gregory Kaziboni came close to firing Nuneaton ahead.
The Pics did start to get a hold of the game as the first half drew on and nearly got ahead when Richard Batchelor’s header bounced on the goal line before being cleared.
Sam Whittal then tested Tony Brendan from distance before Breedan made a great save at his near post to deny Callum Coyle.
After the break, Nuneaton started strongly but it was Rushall who nearly broke the deadlock. Great hold-up play and delivery into the box from Richard Batchelor who found Rahkeem Reid with a powerful diving header but once again Breedan was there to turn it away.
As the second half continued on, both teams felt that the points were there to be taken but neither side could find the clinical edge as they settled for a share of the points.