This is something I am not sure of. Does Azure premium function provide zero downtime deployment by default. In theory there is at least one premium function always up and running, so the new version is deployed as a new instance and the old one is killed after its ongoing request are completed is that even possible.
Thanks in advance. If I find any blogs supporting zero down time, I will add it here.
Not only premium hosting plan, you have to take care of few things like Function time out, use deployment slots and swapping feature when deploying new versions of your function app to avoid downtime, can use durable functions to achieve a zero down-time deployment. Refer the following docs: roostech article1, durable-functions-zero-downtime-deployment strategies and the official doc of AzF deployment slots
Even Azure Functions Premium plan has cold start sometimes.
Even we set the prewarmed instances, when the function is being idle state - it takes some time (few seconds or minutes) to response. In order to reduce that response time also, you can increase the prewarmed instances in
Function App>Scale OutMenu. If you have lot of functionality and code and it is taking more time even in premium, you can raise a Azure Support request.