Silverfish despawn despite being named

I am working on a mob zoo and to keep the mobs spawned in I am utilizing name tags and putting them in the cage. The next mob on my list was a silverfish and I finally caught in in the cage, but when I went out to get a cave spider for the next cage. I came back and found that the sliverfish had despawned. The cage is made out of polished granite so that it wouldn't disappear. I don't know what happened as I have mined every block around the cage and the silverfish wasnt in those either. It was named 23 and now its gone.