The auditors of affected counties may extend the time for the performance of a contract as provided in this section. The contractor may apply, in writing, for an extension of the contract. Notice of the application must be given to: (1) the engineer and the attorney for the petitioners; and (2) for a joint county drainage project, to the auditors of the affected counties. The auditors may grant an extension if sufficient reasons are shown. The extension does not affect a claim for liquidated damages that may arise after the original time expires and before an extension or a claim that may arise after the time for the extension expires.