Well mirc has the option to keep the channels open when disconnect in options, but will not keep the nicks listed in the listbox since your not connected, which makes sence! What you need is to script something that works for you maybe by using the on :disconnect: event.
A quick example for #mirc I used /filter to filter all the nicks from the channel into a .txt file, you could then either open this text file or just filter it to your own @window!
on *:disconnect:filter -cwfl #mirc mircchan.txt | run mircchan.txt
