Thanks for the input. There is a group that isn't having any issues on mIRC at all, on our network. Only our group. We can see that our handshake (not sure this is the right technical term) is being sent out but nothing is received from the distant client.

When mIRC is opened, it connects up until the "message of the day" page and then disconnects immediately.

We are going through some firewalls that we "think" we have mitigated, our routing is going through an ASR, then to a Inmarsat and landing at the far end. We can see that the clients ARE connecting but just can't get the connection to remain.
We're still trying to track down the issue.