Oxaloacetate concentration is by far one of the major contributing reasons as to why a low carbohydrate diet should be supplemented with carbohydrate refeeds. Through ketone use we gain access to increased levels of acetyl Co-A this in term can be synthesized into oxaloacetate via citrate synthase. However in prolonged periods of carbohydrate exclusion there will be a dramatic increase in acetyl Co-A which will not be readily synthesized into oxaloacetate as enzymic reaction will slow down due to homeostatic control of less perceived immediate energy intake (low oxaloacetate concentration).
Carbohydrates provide our liver with available oxaloacetate which can also be readily converted back to acetyl Co-A. This is useful for energy preservation and performance as oxaloacetate plays a major role in glucose metabolism and energy use.
Therefore ensuring that after a period of noticed performance decrease start to include carbohydrate refeed days to restore oxaloacetate concentration thus sustaining a thermocoupling effect of energy output in the mitochondria.
I would base regularity of a refeed dependant on energy requirement. As such a office worker training 4 times a week may only need one refeed as metabolic output will not deplete energy concentration to the point of performance inhibition. In contrast if a bodybuilder or physique athlete were to be doing 7+ hours of high volume training I would recommend a refeed every 3rd day. Refeeds are very personalised and should be modified in accordance to dramatic weight shift, lethargy and inflammatory response. Too little carbohydrate will not do much to restore vigour however too much will also slow gut motility due to excessive hydration caused by over consumption of carbohydrate.
Note also periodising gradual increase of carbohydrate refeed will enable the system to grow accustom to metabolising carbohydrates more effectively and hence reduce inflammation. This in tern will increase potential for greater usable glycogen storage and hence greater metabolic output by increased mitochondrial activation of usable energy substrate.