New generation Industrial Automation and Control Systems (IACS) are providing advanced connectivity features, enabling new automation applications, services and business models in the Industrial Internet of Things (IIoT) era. Nevertheless, due to the extended attack surface and increasing number of cyber-attacks against industrial equipment, security concerns arise. Hence, these systems should provide enough protection and resiliency against cyber-attacks throughout their entire lifespan, which, in the case of industrial systems, may last several decades. A sound and complete management of security issues and software updates is fundamental to achieve such goal, since leading-edge security countermeasures implemented in the development phase may eventually become out-of-date. In this article, a review of the IEC 62443 industrial security standard concerning the security maintenance of IIoT systems and components is given, along with guidelines for the implementation of such processes. As concluded, the security issues and software updates management shall jointly be addressed by the asset owner, service providers and product suppliers. These security processes should also be compatible with the safety procedures established by safety standards.