Hi Carol!
Great question, for which I don't have an answer. Seems like it would take something a very long time to nibble or lick a whole suet cake out of the holder. But then maybe a small raccoon, could take a lot of little chunks out between the cage bars, and maybe do it pretty quickly.
I hate handling those greasy suet cages.
If you can move it to a pole, people use a Slinky on the pole to block squirrels, so maybe that would work on your mystery critter too?