I'm using JupyterHub to share computational power of a big computer among some users. The software that's primarily used is a
Even if you were using straight Jupyter Notebook instead of JupyterHub, each kernel is a single process, that runs kind of independent of the notebook server. Crashes of individual kernels will not take down the notebook server.
Check out the architecture documentation. We've been running a setup with a single Jupyter Notebook instance (not even JupyterHub, because Windows :/) for about 3 years now. The only problems occuring are due to resource constraints (e.g. single kernel takes up a lot of memory), but that's solvable on both the OS and organisational level.