in your error log is the event id 18056? If so and its not causing any issues you can preaty much ignore it (im digging through my bookmarks now to find the link to where Microsoft says its not that much of an issue). you can install the latest CU for your version to quiet the event (It stops the ATTENTION but not the underlying cause)

Best thing to do is look for any bottle necks. Pegged cpu high IO contention slow network. the error is caused when the connection pool relogin throws an exception from what i have been able to gather this can happen when you have a bottle neck or have MAXDOP set wrong (in our case this did nothing YMMV). If you have a bottle neck once you fix the issue it should quit happening.

EDIT:

Here is the blog post i was talking about http://blogs.msdn.com/b/psssql/archive/2010/05/05/error-18056-can-be-unwanted-noise-in-certain-scenarios.aspx

and here is what seems to be the most helpful microsoft connect items: http://connect.microsoft.com/SQLServer/feedback/details/540092/sql-server-2008-sp1-cu6-periodically-does-not-accept-connections