Subsequent DB connections much slower

Our initial, and often our second, connection to a remote database is well within acceptable limits  taking only 1 to 3 seconds.  The problem is with subsequent connections are taking 14 to 23 seconds (see example below).  This problem occurs only with some of our servers and not others, so I do not believe it is related to the remote database.  I am not seeing significant difference in the clients, e.g. same trace level.  Could this problem have snything to do with the way the linux servers are set up?  Has anyone had a simular problem?

$ ./go

13:16:38,637  INFO main dbAccess:25 - getConnection

13:16:39,005  INFO main dbAccess:32 – getStatement                                     1 sec