Strange network connection problem

Ok… I have a department who uses the network connection in a particular meeting room only once a week. It has been working fine for the past year or so. Then, when they tried to use it this week, it didn’t work. They called me over and I did some testing.

I canceled out the possibility of it being the cable by plugging it into a known good port on the switch and using the same laptop they had used. It worked just fine. I then plugged the cable that was in that port into a different port in the switch, and it worked. I switched them, and the problem cable only worked for a minute or so, then stopped working.

Is there some way that the firewall or router is set so there can only be a certain amount of connections active at one time?