Shouldn't the back leg (or at least the back boot) slide? That's one of the major purposes of a lunge.
It may help to try to push the front heel down, and put your body center as far back as you can, consistent with the knee angle.
But I'll leave further advice on that to the experts.
I find back lunges (by which I mean lunges while moving backwards) a lot harder. If I don't get the foot high enough off the ice, I stumble on the blade. For me this is a combination of strength and flexibility. If my muscles were strong enough, I could fight my flexibility limits more easily.