Just leaving him to fall asleep never worked with my DS. He has done it a few times recently in front of the tv, but it's a very rare event. He will just keep going and going and going...
but walking or riding in teh car will generally knock him out, so we do that as a fallback. He needs a lot of help to wind down and even more if he's overtired (as he often is) - perhaps your DD is the same. Does she like books? DS will now do books & bed, though it took some time to get it working (and we still need to do songs & cuddles as well very often)