How long can you leave an Elastrator band on before getting
any permanent damage?

but this says it could happen within the first hour.

Considering they're designed to castrate animals, you might want to be really careful and not leave it on for longer than 30 minutes. I always remove things like this once someone starts to feel numbness.  Numbness indicates lack of blood flow, and whenever there's lack of blood flow, there's potential for permanent tissue damage.

But I wouldn't set a specific time, it depends on the effect that it's having.  You can easily cause permanent damage in 30 minutes under the wrong circumstances.  Watch for symptoms.