Do repeated freeze-thaw strip nutrition from vegetables/food?
Repeated freeze-thaw has virtually no effect on macronutrients, such as proteins, lipids, and sugars, because these are broken down to their basic building blocks (such as amino acids and simple sugars) upon food digestion anyway. 

According to this paper freeze-thaw has no effect on micronutrients, such as vitamins, as well.  

What affects nutritious quality is the length of time the food remains frozen. Most household freezers maintain a temperature of -20°C. At this temperature, the food doesn't get spoiled by bacteria, but degradation of vitamins still occurs, albeit at a slower rate. This is critical for some unstable vitamins, such as vitamin A and C. But elements such as iron, calcium, zinc, and phosphorus are not affected at all. 

If you want to prevent vitamin degradation for a very long time, you need a freezer that maintains food at -80°C. This is only if you want to keep the food frozen for many months though.