You have several options:
If you've downloaded the Desktop application, you can take advantage of its Offline Briefcase feature. Before you go offline, scan through your Conversations and choose the ones you want to download into your virtual briefcase. When offline, bring up the Desktop application and open your briefcase. Open a Conversation, then make new posts, respond to posts, add documents—in other words, interact just as you would if you were online. When you get back online, just click a button to upload all Conversations with the changes you've made.
While in a Conversation, you can click More, then click Download to download the Conversation to your hard drive. The resulting zip file contains a directory for documents belonging to the Conversation, as well as an index.html file with all the Conversation's posts. (The Offline Briefcase, by contrast, has everything integrated for you.) When you open the index file, you can use the Reply link to respond to a post via email. As soon as you're back online and open your email client, your messages are posted to the Conversation(s).
If you've set your notifications to send an email digest at the end of each day, you can also view that while offline, provided that your email application provides such a mode.