It is not recommended to refreeze anything that has reached the temperature danger zone for longer than four hours. That zone is anything from 41f-140f (f=Fahrenheit)! Bacteria growth slows in temps below 41f and is killed at temps above 140f.
There is a break down in nutritional value from the freezing and thawing process, but it is minimal.
So basically, what I am saying is if the rodent has been dead and left in the food temperature danger zone for more than four hours, discard. But, as long as the internal temperature of the rodent is brought down below 41f for less than four hours and then when thawed, not left in the temp danger zone for for the remainder it's OK.
So to really break it down-down. Let's say you thawed a pinkie at 6pm and you didn't feed it to a snake. Assuming that the pink was killed and immeadiately frozen, you now have roughly four hours to feed that pinkie to your snake. But, after one hour 7pm, the snake has not eaten it. You can then safely refreeze that pinkie for another days use. You have to remember that it was kept in the food temp danger zone for at least 1 hour. So mark it! Now that the rodent is frozen, all bacteria growth has stopped. Freezing does not kill bacteria, it just slows it's growth way way down. Probably in about a half hour after re-introducing it to the freezer, around 7:30 let's say, it should be frozen again.
So the next feeding day comes around. You take that pink out of the freezer. Remember that you only have roughly 2.5 hours left to feed that pink to your snake. That includes thawing and then feeding.
At this point, regardless of how much time the pink was out, there is no more re-freezing time left. You can only re-freeze a food product safely once and that is only if you have enough time left on the four hour clock. That means if the snake doesn't eat it this time, definitely throw it away.
I really hope I didn't confuse you! When I took my food safety class a number of years ago, it took me a bit to figure out what I was being told. I'm also, not that smart.
The long of the short, sometimes it's just better to discard the rodent, then worry about all the jargon I just wrote.
Good Luck, :cheers:
Wayne