Does repeating freeze -> chill -> freeze -> chill spoil yogurt?
I hate yoghurt which has been frozen even once, as the emulsion separates and makes the texture totally wrong. 

But if you don't see any problem with that, the only problem you are left with is food safety. After many cycles, you don't know how much time your food has spent thawed and how much time it has spent frozen. The solution is simple: put the yogurt into smaller containers, freeze them, and take out a single container for each use. 

By the way, 3 kg of yogurt isn't that much, seeing that yogurt keeps for many weeks in a fridge. With a few yogurt-heavy recipes, you could get it finished without the need for freezing at all.