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].”
Mono causes months of extreme fatigue when symptomatic (first study I found says 72% of infected patients had fatigue), this study says 4% of high schoolers met the conditions for Chronic Fatigue Syndrome 24 months “after infectious mononucleosis” (unclear if that’s after diagnosis or what). In that study 11⁄13 cases improved between 12 and 24 months, but 2 were worse. 24 months out was the longest I could find: lots of studies showed extreme fatigue at 6 or 12 months but that seems more like a slow recovery that chronic infection.
Mono is unlikely to be a good model for COVID-19 because the infection is permanent, like chickenpox, whereas I believe coronaviruses are typically fully cleared.
Pandermix, an H1N1 vaccine, is general considered to have led to an increase in rates of narcolepsy, especially in humans. None of the studies I found even mentioned relative risk except for this critical survey, done by people receiving money from the vaccine manufacturer.