As mentioned above. I did not find the way how to get from parent window object its child windows. Probably nothing like window.childWindows array or method exists. After reloading parent page you even lost all binding created with javascript like childWindow = window.open(url,'myChildWindow',opt)
Only possible way I found for FF 3.x is in case you know the name of child window you are looking for. In this case open window again with the same name and if it is still open you should get the lost link. In other case the new window is open.
lostWindow = window.open('','myChildWindow','');
Now you have to test if it is your old window or the new one. For example by some attribute you registered in your child window.
if (lostWindow.myProperty == 'yes')
you can be quite sure it is your lost window.
As I was looking through internet i found some people try to create workaround with cookies or in HTML5 with applicationCache
.