Connectivity issue in Stateful app database using VPA

We are using an autopilot Kubernetes cluster and we have deployed cockroach DB stateful app with a minimum of 3 pods in that cluster. I am testing VPA for that database for auto-scaling. But When the pod hits the defined limit in VPA it’s recreated and due to that our application throws DB connection errors till the pod is not up. Is that any proper way to an auto-scale Stateful Applications graceful way so that each pod while coming down completes its pending tasks and then gracefully shutdown pod that database connections are not affected?

Kubernetes version: 1.20.10-gke.301