No, normally there is no expectation of a time limit on the performance of a contract. If there is, it must be negotiated at the time the contract is formed

.You should be able to sign a contract at any time. Most contracts do not require a certain time of the day for the contract to be signed. Many contracts have a time limit

A new contract with new consideration would need to be agreed upon

there is no cut-off time for a contract unless it included a 'time is of the essence' clause.

If you want to sue under a contract, it should be within two years of the time you should have known there was a breach.

Serve a notice to complete on the other side, stating that time is of the essence, clearly indicating the time, date, place, etc for completion/ performance of the contract