Can fat loss cause A1c rise?

Fats slow the absorption of carbs.  When you take too many fats out of your diet - you have all carbs and they are processing faster.  This means high sugar spikes after every meal.  That causes your A1C to go up.

BTW - the body stores carbs as fat.  Eating fat does not make you fat - it is the carbs.  

There is always some chance that you would have had a raise in A1C no matter what you did.  Some people become a type 2 diabetic no matter how they try to avoid it.  

I did some research for you. Per the source article below "Losing weight is the first step to lowering your A1c."  (link 1)

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Remember eating fat doesn't make you fat. Link 2 gives guidelines on what to eat to help lower your A1c and it includes "eating a balanced diet complete with healthy proteins, fats, and carbohydrates".