how do you know that contacting them is getting difficult ffs? its not you and its not your client. neither of us have any idea of the terms that the contract was entered into, the value of the contract or the working relationship - all these things need to be considered before you tell someone to 'take the site down'.
all i'm saying is, in the real world, 60 days is still quite common. get used to it now to avoid tears later.