Analyzing packet loss, whether resulting from communication challenges or malicious attacks, is vital for broadcast authentication protocols. It ensures legitimate and continuous authentication across networks. While previous studies have mainly focused on countering Denial of Service (DoS) attacks' impact on packet loss, our research introduces an innovative investigation into packet loss and develops data recovery within variant TESLA protocols. We highlight the efficacy of our proposed hybrid TLI-µTESLA protocol in maintaining continuous and robust connections among network members, while maximizing data recovery in adverse communication conditions. The study examines the unique packet structures associated with each TESLA protocol variant, emphasizing the implications of losing each type on the network performance. We also introduce modifications to variant TESLA protocols to improve data recovery and alleviate the effects of packet loss. Using Java programming language, we conducted simulation analyses that illustrate the adaptability of variant TESLA protocols in recovering lost packet keys and authenticating previously buffered packets, all while maintaining continuous and robust authentication between network members. Our findings also underscore the superiority of the hybrid TLI-µTESLA protocol in terms of packet loss performance and data recovery, alongside its robust cybersecurity features, including confidentiality, integrity, availability, and accessibility. Additionally, we demonstrated the efficiency of our proposed protocol in terms of low computational and communication requirements compared to earlier TESLA protocol variants, as outlined in previous publications.