I've had rabbit issues for years and my experiences are the same as yours. I was thinking along the lines of a larger type rodent too, though never had a problem with gophers or groundhogs. Have not seen tunnels of any sort. The leaves aren't eaten on these stems, nor do they eat the buds once the lily is felled.
Another weird thing is that we've seen several of these hourglass- shaped spots in the yard in the last few weeks. Likely from urine; burned, but the grass isn't killed.
No Diann, it's not Harvey.
