As I was desperately trying to come up with a solution for the last disaster, I attempted sewing velcro onto the chair seat kinda like this.
I did end up having enough to weave the other seat (yay!), so we have two chairs again! We've actually had two chairs again for almost a week, I've just been terribly slow trying to keep up with the blog lately.
Oh, and if you want tips on weaving a chair seat out of fabric I would suggest going to the chair weaving tutorial at First a Dream. I read through that before I started mine and it was helpful. I made my strips quite a bit wider than hers so it really didn't take me very long.