Why does viral RNA sometimes persist after recovery from acute infections?

DNA viruses often persist in the body of their host, becoming latent and recurring many months or years later. By contrast, most RNA viruses cause acute infections that are cleared from the host as they lack the mechanisms to persist. However, it is becoming clear that viral RNA can persist after clinical recovery and elimination of detectable infectious virus. This persistence can either be asymptomatic or associated with late progressive disease or nonspecific lingering symptoms, such as may be the case following infection with Ebola or Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). Why does viral RNA sometimes persist after recovery from an acute infection? Where does the RNA come from? And what are the consequences?