Intuitively, one might expect that viruses which cause fatigue during acute infection are more likely to also cause chronic fatigue later. Is this in fact the case?
COVID-19 causes fatigue in about 70% of cases according to one study (though studies have had mixed results, most likely due to sampling patients at different levels of severity and differences in how symptom lists are collected).
Note that while there is pretty good data about the symptoms of viruses on presentation, data on chronic fatigue is relatively poor. So, a good answer to this question might look like “human examplevirus infects 20% of the population[cite1], causes fatigue 30% of the time[cite2], and is implicated in chronic fatigue on questionable patient forums[cite3].”