From what I've been reading on the forums and the FAQ, it appears that BitCoin will simply pick up where it left off if the client is shutdown or can't communicate with the network.

In fact, it may even be that it will continue to calculate, but just won't be able to retrieve the most up-to-date information from other nodes, nor communicate out to those nodes. So if you forget to log in and stay offline for a while, then yea... you'd probably be hosed.