If you have a "man in the middle" then there are deeper problems, like, you're using a compromised network.
We do actually cycle part of the cookie every so often, so if someone has an old cookie of yours it probably won't work. That's assuming they stop listening, and you keep using the site.
Also, we don't think the risk of someone stealing your Stack Overflow account is very dangerous compared to, say, your online banking account, or your gmailGmail. (rememberRemember email is the de-factode-facto skeleton key for all online logins that I know of).)