Currently, if cookie-authentication is used for RPC and Bitcoin Core is restarted, the old cookie fails to authorize (reported in #48). If this happens, it might be worth trying to reload the cookie file once to see if that helps. I'm not sure if that's doable within the current rust-bitcoincore-rpc setup, but it can't hurt to try.
RPC users and password auth is not affected and should work across restarts.