Do I need to shut the whole system down if there is a problem?

No, each unit can be wired to operate independently.  Heater elements have a typical lifespan of between 7-10,000 hrs depending on use.   

Any fault in one heater can be isolated and replaced/repaired while the other heaters continue to operate.  

Modular design of elements within heaters, allows for quick replacements or repairs on site enabling elements to be changed easily and quickly.