Depending on your setup it might be a problem with Spanning Tree, of you have redundat links or layer2 loops it is advisable to configure a switch to be spanning tree root. (this is per vlan).
Another problem I have seen in the past is auto negotiation, this can also provide problems.
You should look at port statistics. And see if there are any errors.
I presume there is no router or firewall in between the users and the telnet servers. They could be configured to disconnect sessions after a certain time.
To give you a better answer, I will need some more information