Neon's serverless Postgres solution offers compatibility with both serverless and traditional long-running applications. Its auto-suspend feature can reduce database costs during off-peak times by suspending databases when no activity is detected within a specified time window. To handle connection loss, client-side pooling can be used to manage the number of open connections and improve performance. This solution benefits both serverless and long-running applications, making them more resilient to connection errors and reducing costs for non-production environments.