"No buffer space available" Socket Errors on Windows Server 2003 SP2

I have a box I use for network management. Recently I applied SP2 to
Windows Server 2003, and I also have added a syslog daemon
(KiwiSyslog). It also runs a number of other services, including
BackupExec 11d, EventSentry, Paessler PRTG, Track-It, and GoodLink
Server.

Some time ago (not sure when in relation to the above or other
changes, unfortunately), the system after its been running for a few
days loses its ability to make outbound TCP connections. This shows
up in the logs as individual application failures, including
GoodLink's XML service, EventSentry's ODBC connection to another SQL
server, Track-It's SMTP and POP connections to Exchange, and so on.

Some of these applications will record an error when they fail to
connect that includes the message "No buffer space available". Other
application errors include "OdbcExpandError: [01000] [Microsoft][ODBC
SQL Server Driver][TCP/IP Sockets]ConnectionOpen (Connect()).
(10048)", "Unable to bind to socket (10055)", and "The RPC server is
unavailable" depending on the app and operation.

Rebooting restores service immediately. But I'd like to diagnose and
resolve this.

I've disabled the KiwiSyslog service for the moment to see if I can
isolate one app at a time, but that's time-consuming.

Is there some way to identify what's going on here? I see references
to this error message going back quite a ways in the WinSock world, so
I'm wondering if there's a poorly-behaved application that isn't
releasing resources or something similar. If so, how to diagnose?