Partially defrosting, then refreezing?
If you're unthawing them in your refrigerator (below 40 F), then you should be just fine. Most beasties don't reproduce at any significant rate below 40 F.

There isn't a clean cut off point because it depends entirely on the existing level of contamination present in your meat. 

You should be aware that repeated cycles of thaw/freeze will really damage the texture of your meat. The cells simply do not hold up to that.