Why take it down? It still gives facebook users who want to show support for your comic a way to do so.
I link my facebook pages from my site proper, and use a facebook app (rss graffitti) to automatically update the pages with the latest comments.
When someone "likes" the page, they get occasional reminders then - getting them to come back to the site. It's all about retention, and if you do it right, it takes little to no effort.
That said, you have to remember that Facebook doesn't show every update to everyone who's a fan. Don't tell people to rely on the page.