Sixteen games without a win and defeat at bottom club Dagenham on Saturday mean the Silkmen are above the relegation zone on goal difference only, two points and two places behind the Cobblers.
Brian Horton has taken charge until the end of the season.
Six successive losses have also seen Burton Albion, Northampton's midweek opponents, axe their manager Paul Peschisolido while, on a day of casualties in League Two Rotherham and Andy Scott have also parted company.