We consider applications involving a number of servers in the cloud that go through a sequence of online periods where the servers communicate, separated by offline periods where the servers are idle. During the offline periods, we assume that the servers need to
securely store sensitive information such as cryptographic keys. Applications like this include many cases where secure multiparty computation is outsourced to the cloud, and in particular
a number of online auctions and benchmark computations with confidential inputs. We consider fully autonomous servers that switch between online and offline periods without communicating with anyone from outside the cloud, and semi-autonomous
servers that need a limited kind of assistance from outside the cloud when doing the transition. We study the levels of security one can - and cannot - obtain in this model, propose light-weight protocols achieving maximal security, and report on their practical performance.