Research software is an integral part of most research today and it is widely accepted that research software artifacts should be accessible and reproducible. However, the sustainable archival of research software artifacts is an ongoing effort. We identify research software artifacts as snapshots of the current state of research and an integral part of a sustainable cycle of software development, research, and publication. We develop requirements and recommendations to improve the archival, access, and reuse of research software artifacts based on installable, configurable, extensible research software, and sustainable public open-access infrastructure. The described goal is to enable the reuse and exploration of research software beyond published research results, in parallel with reproducibility efforts, and in line with the FAIR principles for data and software. Research software artifacts can be reused in varying scenarios. To this end, we design a multi-modal representation concept supporting multiple reuse scenarios. We identify types of research software artifacts that can be viewed as different modes of the same software-based research result, for example, installation-free configurable browser-based apps to containerized environments, descriptions in journal publications and software documentation, or source code with installation instructions. We discuss how the sustainability and reuse of research software are enhanced or enabled by a suitable archive infrastructure. Finally, at the example of a pilot project at the University of Stuttgart, Germany -- a collaborative effort between research software developers and infrastructure providers -- we outline practical challenges and experiences