That's what I'd worry about, too. In the past I've built raised bed boxes with chicken wire mesh on the bottom stapled to the inside of the box. I've then wrapped chicken wire around the outside, stapling down securely on three sides and leaving it partly unstapled on the third so I could pull it back for access. By wedging bricks up against the unstapled wire I was able to make it fairly rodent resistent -- except for the squirrels, of course. They teleport.