As food is thawing out it will start to build up bacteria. The warmer it gets the faster the bacteria builds up. When the bacteria population is high enough it will make you sick.
When you refreeze the food it doesn't kill the bacteria. The bacteria basically goes into hibernation. As you thaw food for the second time all the bacteria built up after the first thaw will become active and start multiplying again. Because the bacteria population is much higher when you thaw it the second time it will reproduce faster and is more likely to reach the danger threshhold.
It really depends how warm it got, whether it was sealed, and how long it was warm for.
Human food you can cook, which kills the bacteria, and then refreeze, but I don't think I'd want to do that to fish food