Background: During COVID-19 pandemic, service providers and beneficiaries of Rashtriya Bal Swasthya Karyakram (RBSK) faced certain challenges. Objectives: The objective was to assess the perception and challenges faced by service providers and beneficiaries in general and amid the pandemic for availing the services at an urban health center in Ahmedabad. Methodology: Data of registered cases under RBSK at Urban Health Center (UHC) Ognaj in 2018–2019 and 2019–2020 were compared. In depth interviews (IDIs) of Medical Officer RBSK were done. Home visits were done to document the perception and challenges of beneficiaries through semi/unstructured questionnaire. Results: Considering the cases of 2018–2019 as base, registered cases decreased by 22.8% in 2019–2020 and 92.4% in 2020–2021. The pandemic affected 15.6% of beneficiaries in availing the services. Program was affected due to: (1) less workforce (vacant pharmacist post), (2) target-based approach, and (3) birth defects, deficiency disorders, chronic diseases, and development delays, especially deficiency not perceived a serious health issue by beneficiaries. Corona-specific reasons included: (1) staff deployment in COVID-19 activities, (2) reluctance/fear in visiting District Early Intervention Center (DEIC)/health facility, (3) reduced screening due to the closure of schools/Anganwadi Kendras, and (4) enforced lockdown. Conclusions: RBSK mobile health teams found it difficult to reach all 4Ds, more so for follow-up. RBSK was badly affected due to the engagement of providers in COVID-19 work, the closure of facilities, perception of beneficiaries that 4Ds are not of urgent medical concern, prevailing myths. A clear strategy is required to address such problems when the same or a similar type of pandemic strikes us in future.