The problem you are having is because of bad sessions on JDBC Pools
Setting the min connection value to 0 permits the pool to close all connections in the pool after the idle/expiration time has passed. This is the recommended setting for production environments. This avoids keeping unused connections too long and helps avoid stale connections (Stale connection : connections that the adapter thinks are still good but the resource has closed.)
This setting does not control the number of simultaneous connections allowed. That is controlled by the max connections setting.
I would like to keep a connection pool to 1 in terms of realtime services like webServices. When a webService tries to connect to a db it should have data readily available.
Hope this helps.
#Integration-Server-and-ESB#webMethods