Cloud Radio Access Networks (Cloud-RANs) have recently emerged as a promising architecture to meet the increasing demands and expectations of future wireless networks. Such an architecture can enable dynamic and flexible network operations to address significant challenges, such as higher mobile traffic volumes and increasing network operation costs. However, the implementation of compute-intensive signal processing Network Functions (NFs) on the General Purpose Processors (General Purpose Processors) that are typically found in data centers could lead to performance complications, such as in the case of overloaded servers. There is therefore a need for methods that ensure the availability and continuity of critical wireless network functionality in such circumstances.Motivated by the goal of providing highly available and fault-tolerant functionality in Cloud-RAN-based networks, this paper proposes the design, specification, and implementation of live migration of containerized Baseband Units (BBUs) in two wireless network settings, namely Long Range Wide Area Network (LoRaWAN) and Long Term Evolution (LTE) networks. Driven by the requirements and critical challenges of live migration, the approach shows that in the case of LoRaWAN networks, the migration of BBUs is currently possible with relatively low downtimes to support network continuity. The analysis and comparison of the performance of functional splits and cell configurations in both networks were performed in terms of fronthaul throughput requirements. The results obtained from such an analysis can be used by both service providers and network operators in the deployment and optimization of Cloud-RANs services, in order to ensure network reliability and continuity in cloud environments.