From version 7 onward, the Application Server scripts and configuration scripts have the good manner to set by themselves the right ulimit valu. So ulimit is now less a problem than it was before. The problem is that, sometime when dealing with linux services,things do not always get right.
For example you get exceptions such as
[11/14/13 12:06:15:483 CET] 00000066 exception E com.ibm.ws.wim.adapter.ldap.LdapAdapter authenticateWithPassword
com.ibm.websphere.wim.exception.WIMSystemException: CWWIM4520E The 'javax.naming.CommunicationException: ldapus.ldap.domain.com:389 [Root exception is java.net.SocketException: Too many open files]' naming exception occurred during processing.
(In case you are asking, yes, network connections are counted as open files)
That's why I strongly suggest to modify your /etc/security/limits.conf (on RedHat) before restarting your machine, after you added WASService.sh service to your linux box. We added to the file the following two lines to the /etc/security/limits.conf
* soft nofile 32768
* hard nofile 32768
and then restarted the machine and had my Connections environment working.