Trend Micro shares some excellent user safety tips and administrative design standards to help mitigate attacks.  One key practice is to close secure websites by logging out to keep sessions as short as possible.

BEAST and TLS/SSL Security: What It Means For Users and Web Admins
http://blog.trendmicro.com/beast-and-tlsssl-security-what-it-means-for-users-and-web-admins/
What can users do?

• Keep time spent on sensitive SSL sessions as short as possible. The attacker needs time to decode the encrypted message. If the session cookie is invalid before the attacker has finished, this attack fails.

• When leaving an SSL protected site, be sure to actually log out, not just move to a new site. In many cases, actively logging out will invalidate any cookie/session data that the attacker may have successfully decoded.

• Standard security best practices still work. For this attack to be successful, the attacker must have access to either your network or your computer. At the very least, up-to-date security software will make life harder for an attacker.
What can website administrators do?

• Make sure your logout button performs the expected action. You are leaving users at risk if your site does not actually invalidate session cookies when they click “log out”.

• Ensure that session cookies are tied to an IP address where the session was established. If that IP address changes, consider validating that the source of the requests is still your user. This will not prevent this attack, but it will make it harder to exploit your users.

• Resist the temptation to change SSL ciphers without carefully considering the risks first. While it is true that RC4 is not subject to this attack, it presents more risk than AES. Also, it isn’t a bad idea to keep an eye on the IETF TLS working group.  New versions of the TLS standard exist that eliminate the weaknesses used in this attack. Unfortunately HTTP server and browser coverage of these new standards is spotty at the moment at the moment. So you have to carefully consider both your environment and your user base before such a change.

TLS (Transport Layer Security) Working Group
http://datatracker.ietf.org/wg/tls/charter/