The company ran into financial trouble last month after being in business since 1591.
Brighton and Hove City Council said the firm was no longer working on its £21m Dome Corn Exchange and Studio Theatre refurbishment after it had “ceased trading”.
But the company has now struck a company voluntary arrangement (CVA) with its creditors brokered by Begbies Traynor.
Documents filed at Companies House show creditors owed more than £8m have agreed to give Durtnell more time to pay its debts under the CVA.
Latest accounts filed at Companies House show R Durtnell made a pre-tax loss of £700,000 from £51.6m turnover in 2017.
During that year the company employed 108 staff.