Excellent idea!
To be generous, I would suggest sellers have to log on 1x a week (except when on holiday). That gives leeway for those in situations where they have to work 60-80 hour weeks, or only get access to a computer 1x a week.
I am also thinking it would be a good idea on every auction listing to add a brightly visible rectangle that states: "Seller Last Logged In to Ebid", and gives the day and hour. I'd put this right under the "Watch This Auction" and "Ask a Question" buttons. And I'd color code it: it turns green when the seller has logged in in the past 48 hours, yellow when it's been 4 days since the last log on, and red when it's been more than a week since the seller has logged on. The holiday setting would turn it red, too. The fine print under this rectangle would explain the meaning of each color. This would make it easy even for newbies to quickly see if the seller is active.
I recently tried to get an answer about postage for multiple items from a seller, and it took about 6 days to get the first response, and then 4 days to get the answer back from my response that day to her question about my question. That seemed dreadfully slow to me, and I think would have been off putting for a newbie.