The fact that your database is reachable but the app isn't after restart points to the routing layer being toast. If you can ssh into the dyno or check logs, look for anything related to the router handshake timing out. Usually when deploys work but traffic doesn't route, it's something between the load balancer and your instances.

The correlation with scheduled restarts is interesting though. Makes me wonder if there's a cert validation issue on boot that's causing new instances to fail health checks.