If a contract does not contain a Time Is of the Essence clause can you go past your original closing date?

Absolutely, as long as the party responsible for the delay is working to solve the issue/problem. The courts use the "reasonable man" idea for this. If you are going past a closing date more than 30 days--that is different than 10 days or two weeks. Most new construction contracts give the builders 30 to 60 days past the projected contract closing date.