btt...
Define 'stable'.
AmigaOS by itself is stable. By running the OS and its various tools coming along with it it's hardly possible to crash it.
However, when adding software, tools and applications it can be made to crash quite easily - a single severe bug in any application is sufficient. There's no protected memory and trashing kernel memory is bound to sink the system, a complex multitasking system being much more delicate than a simpler OS.
In order to overcome this, memory protection and a decent HAL would need to be added (which isn't possible without extensive changes to the system as has been discussed adequately).
But as can be seen in MS Windows (NT), this may not even be enough. Windows drivers are still required to run with Ring 0 privileges where they may do whatever they like. Any driver bug can still crash the system. Is this better? Definitely. Is it stable? It's more stable but you're still short of 100%.