Will Licensing Service prevent connections to Win Server 2003 std?

Hey everyone, at this site we have two Windows servers, both 2003 standard edition, one of which is R2. The R2 is acting as print server for approx. 50 users. Well last week that server went down and would remain that way for a couple days so I set up a number of temporary printers on the other server (who's primary role is a file server) and redirected users to those shared temporary printers. Later on that day a few users started complaining that they couldn't reach network shares or access shared printers. I quickly discovered that I was somehow exceeding the number of connections available on that server and resolved the issue by periodically closing un-needed network connections to the working server until the disabled machine was restored.

I'm running the Licensing Service to make sure that I'm in compliance (have enough CAL's to meet the number of connections to the server) in Per Server mode. I was under the impression that the Licensing Service was simply a monitoring tool and would not actually prevent connections past the number of CAL's available. Am I mistaken about the licensing service or is it possible that I'm reaching the performance limit of this particular server and reaching the number of connections that it can handle?

Here's a quick hardware summary of the server in question:
Dell PowerEdge SC1420 running Win Server 2003 Std Edition x86
CPU: Xeon 3.00GHz
Memory: 3GB DDR2
NIC: Intel, 1Gbps connection

With 20-30 connections open for file shares and another 20-30 for printing service is it possible that I'd asked too much of that machine and as a result it could not accept new connections? Is this the way an over-taxed system would prevent itself? I usually monitor basic server performance stats but of course the server that runs PRTG network monitor was the one that went down so I don't have any performance history for the server in question when it was under load...

Thanks in advance for the advice