No More Connections ….

I am getting the following message:
‘NO MORE CONNECTIONS CAN BE MADE TO THIS REMOTE COMPUTER AT THIS TIME. THERE ARE ALREADY AS MANY CONNECTIONS AS THE COMPUTER CAN ACCEPT’ when trying to access 2 other computers (none are servers) on my local network from an XP Pro system.

Microsoft’s KB815432 says to install SP2. I installed SP2 a long time ago and the problem went away. When I updated to SP3, the problem came back.

Help … please and thank you.