This would make your CMS log packets. ctrl+c to stop.
tshark -i eth0 port 22 -w /tmp/myssh.pcap
Honestly, what I'd suspect is the CMS Supervisor session is locked up. You'd get that "other end reset the connection and dropped" if you logged in with CMS Supervisor on one PC while in on another. You could still ssh via putty. The difference - even though both run on port 22 - is that putty is just a terminal and cms supervisor invokes the application. You'd equally fail to log in to CMS Supervisor with the 'cms' user account.
Here's another silly idea: I've been in environments where there's some firewall doing session or packet inspection. Leave a putty terminal up for >5 minutes and it kills it - but not gracefully - my CM terminal is dead, not responsive and a few minutes after a key press, then it'll timeout. Maybe people leaving it on overnight without a realtime display going (or something to cause real traffic all the time) would make some security stuff in between the PC and the CMS kill the connection ungracefully and not releasing the CMS Supervisor session gracefully causing it to lockup.
maybe next time a user has it happen, do a 'netstat -tunap |grep 22' in cms would show you all established sockets on that port, and if the person's IP is in there with CMS closed, and can't log in with their account, and can login with some other user's account from the same PC, then I'd look at SSH in your network more than on the CMS server.