Background/Objectives: This study aimed to evaluate sociodemographic factors, features of the acute infection, and post-infection health status in survivors of COVID-19, assessing their association with post-acute COVID-19 syndrome (PACS). Methods: A multidisciplinary public clinic in Brazil assessed COVID-19 survivors between June 2020 and February 2022. Patients were classified as having PACS or subacute infection (SI). Data on the history of the acute infection, current symptoms, physical examination, and laboratory findings were collected and analyzed using multivariate models with PACS as the outcome. Results: Among the 113 participants, 63.71% were diagnosed with PACS at a median of 130 days (IQR: 53–196) following acute symptom onset. Admission to the intensive care unit was more frequent among individuals with PACS than those with SI (83.3% vs. 65.0% respectively; p = 0.037). Symptoms significantly more prevalent in the PACS group when compared to the SI cohort included hair loss (44.4% vs. 17.1% respectively; p = 0.004), lower limb paresthesia (34.7% vs. 9.8% respectively; p = 0.003), and slow thinking speed (28.2% vs. 0.0% respectively; p < 0.001). Logistic regression revealed that only the time interval between the onset of acute symptoms and the clinical evaluation was independently associated with a PACS diagnosis (β = 0.057; 95% CI: 1.03–1.08; p < 0.001). Conclusions: Patients with PACS had a higher frequency of intensive care unit admission compared to those with subacute infection. However, in the multivariate analysis, the severity of the acute infection did not predict the final diagnosis of PACS, which was associated only with the time elapsed since symptom onset.