Error 18456 Serverity 14, State 38
One location for finding out about many of these states is a post by Aaron Bertrand at:

https://sqlblog.org/2011/01/14/troubleshooting-error-18456

The error you are asking about are:

Error: 18456; Severity: 14 State: 23
Access to server validation failed while revalidating the login on the
connection.
Error 18456; Severity 14; State 38Failed to open the database specified in the login properties. (or)  Cannot open database &quot;&quot; requested by the login. The login failed.
Error 18056; Severity: 20, State 23

This is apparently related to connection pooling when the client could not reuse a spid.   If this is the same problem you can look at this Microsoft Connect item, but it has been closed as &quot;Not Reproducible.&quot;

https://connect.microsoft.com/SQLServer/feedback/details/468478/sql-server-2008-periodically-does-not-accept-connections

and then:

Error 18451, Severity 14; State 1

SQL Server is in the process of shutting down. During shutdown, only members of the sysadmin fixed server role can make new connections.

This suggests that your installation needs some examination and perhaps updated to a more recent patch level.