Immunotherapy for Neurological Post-Acute Sequelae of SARS-CoV-2

Study Description: This study will evaluate the clinical and laboratory effects of immunoglobulin therapy in patients who recovered from acute mild-moderate COVID-19 infection but still have persistent neurologic symptoms. Despite clinical recovery from the acute infection, some individuals continue to experience ongoing symptoms, at times several months after recovery, and many of these symptoms are neurologic. Some features suggest that this is a post-infectious immune-mediated process, and anecdotally patients have responded well to immunoglobulin therapy. This study will evaluate the clinical and laboratory effects of intravenous immunoglobulin therapy compared to placebo using a cross-over trial design. It is hypothesized that immunoglobulin therapy could have positive clinical and laboratory effects on patients with persistent neurological symptoms. Objectives: Primary Objective: To compare the clinical efficacy of intravenous immunoglobulin therapy to placebo in ameliorating the neurological post-acute sequalae of SARS-CoV-2 infection. Secondary objective: To determine the clinical effects of intravenous immunoglobulin therapy in patients with neurological post-acute sequalae of SARS-CoV-2 infection. Exploratory objective: To investigate the laboratory effects of intravenous immunoglobulin therapy in patients with neurological post-acute sequalae of SARS-CoV-2 infection. Endpoints: Primary endpoint: Proportion of participants with a clinically meaningful change in Health Utilities Index Mark 3 (HUI3) 2 weeks after intravenous immunoglobulin therapy compared with 2 weeks after placebo. Secondary endpoints: * Change in functional / patient-reported scales: * WHO post COVID-19 functional scale * Post-COVID-19 Functional Status (PCFS) scale (0-4). * COVID-19 Yorkshire Rehabilitation Scale * PROMIS Global Health score * PROMIS Depression score * PROMIS anxiety score * Change in clinical scales: * Montreal Cognitive Assessment (MoCA) * Brief tablet-based Neuropsychiatric evaluation * Karnofsky Performance Status (KPS) Exploratory endpoints: * Autonomic testing - Change in the number and character of test results indicating autonomic nervous system dysfunctions as evidenced by abnormal physiological responses to the Valsalva maneuver or head-up tilting. * Change in immunological markers: * Cytokine levels * Cell markers per flow cytometry * SCENTinel, Olfactory testing, Monell