Of course to cure from a fever in general takes already time to recover from, but in the kissing disease it takes often much longer (sometimes even years) and the tiredness is much more a symptom of the Epstein virus than other virus infections. But what causes this precisely?
There is no consensus on the exact cause, although in Chronic Epstein-Barr Activation (CEBA) it has been linked to the effects of inflammation (eg a cytokine storm), plus immune activation and tryptophan degradation.
In the more common, non-CEBA Epstein-Barr infection immune system responses are also suggested to be linked to the fatigue. "Presently, therefore the is no proven fatigue-causing substance or fatigue transmitting substance. However, the most probable candidates for such fatigue-inducing or fatigue transmitting substances are cytokines, including interferon."2
Lasting fatigue is found in a number of viruses, including a number of Covid-19 patients.3 This may be related to Interleukin-1 levels, an inflammatory cytokine.
Long term fatigue is often termed "Chronic fatigue", "post-fatigue infection" or "post-viral fatigue" (without the syndrome part).
According to Emedicine medscape:
Appreciate that EBV may trigger chronic fatigue, but it does not cause chronic fatigue.
In their page on Chronic Fatigue Syndrome:
CFS is a biological illness, not a psychologic disorder. The exact pathogenesis is unknown. Numerous mechanisms and molecules have been implicated that lead to abnormalities in immune dysfunction, hormonal regulation, metabolism and response to oxidative stress to include impaired natural killer cell function and/or T-cell function, elevated cytokines, and autoantibodies (rheumatic factor, antithyroid antibodies, antigliadin, anti–smooth muscle antibodies, and cold agglutinins). [3, 4] Infections have been suspected; however, no causal role has been established.
The sources cited: