I think a rota is a good idea - but I think it should be a loose one, so that any admin who happens to be online feels free to 'like' and respond to posts, or to add something that's particularly interesting.
Also (this is the selfish bit) I'm a little worried about promising to be 'on duty' at particular times, as I'm mostly checking in when I have a minute at work, or for a short while at a time (when I should really be playing with dd or talking to dh after I get home). I'm sure it's the same for all of us.
I'd be happy to take a day or two, or a particular timeframe of each day, when I know I need to check in and make sure things are updated, but I'd feel better about that if I knew that other people might also be dipping in and out (as I will be on my 'off' times) and so if I can't be on as much as I want, things are still likely to be posted / reponded to.
I think the response thing is important - when people post to Facebook I think we have to be sure to 'like' or comment on their post fairly soon after, so they know we appreciate the interest and we're still here! There will be exceptions, of course - I've noticed that when a point has needed to be argued, the argument has been between 'likers' / under people's own names rather than the page name, which is a good way to go.