Background/Objectives: Children with chronic diseases and their families face significant challenges to their quality of life compared to the rest of the population, and the COVID-19 pandemic has been a greater challenge for them. Our research aimed to identify key factors affecting their quality of life. Methods: We conducted a cross-sectional study in the Department of Pediatrics of the “Grigore Alexandrescu” Emergency Children’s Hospital in Bucharest on a group of 47 pediatric patients aged 9 years or older, diagnosed with chronic liver, gastrointestinal, and pancreatic diseases. Results: Children reported that their quality of life was not significantly affected by the pandemic due to the inability to see their family members and friends (89.36%), online education (67.5%), and social distancing (50%). Results showed that parents’ perceptions of the COVID-19 pandemic had a significant negative correlation with their quality of life (r = −0.35, p < 0.01); also, parents’ perceptions of the quality of life had a high negative significant correlation with their children’s mental well-being (r = −0.67, p < 0.001). Interestingly, children’s mental well-being did not have a significant correlation with their perceptions of quality of life (r = −0.02, p > 0.05). In the context of the COVID-19 pandemic, parents were concerned about their family well-being. Parents with higher scores for the perception of COVID-19’s impact tended to have lower scores for health-related quality of life. Also, the parents’ quality of life accounted for 44% of the variance in their children’s mental well-being. Conclusions: Even if the medical issue of the COVID-19 pandemic was not a concern for either children or their parents, many families were anxious about the perceived lack of dependability of the medical system. Addressability was delayed in many cases because of this, and regular medical care is essential for patients with chronic diseases.