A Linux system administrator wears many hats and the smaller your environment, the more hats you will wear. Linux administration covers backups, file restores, disaster recovery, new system builds, hardware maintenance, automation, user maintenance, filesystem housekeeping, application installation and configuration, system security management, and storage management. System administration covers just about every aspect of hardware and software management for both physical and virtual systems.
Oddly enough, you also need a broad knowledge base of network configuration, virtualization, interoperability, and yes, even Windows operating systems. A Linux system administrator needs to have some technical knowledge of network security, firewalls, databases, and all aspects of a working network. The reason is that, while you're primarily a Linux System Administrator, you're also part of a larger support team that often must work together to solve complex problems. Security, in some form or another, is often at the root of issues confronting a support team. A user might not have proper access or too much access. A daemon might not have the correct permissions to write to a log directory. A firewall exception hasn't been saved into the running configuration of a network appliance. There are hundreds of fail points in a network and your job is to help locate and resolve failures.
Linux system administration also requires that you stay on top of best practices, learn new software, maintain patches, read and comply with security notifications, and apply hardware updates. An SA's day is very full. In fact, you never really finish, but you have to pick a point in time to abandon your activities. Being an SA is a 24x7x365 job, which does take its toll on you physically and mentally. You'll hear a lot about burnout in this field. We, at Enable Sysadmin, have written several articles on the topic.