Grafana backend randomly stops responding to requests

Running a standard “production” Grafana, proxied behind a web server and using Influx as datasource.
Version 5.3.4, and Grafana uses the sqlite backend for user management.

Sometimes the process stops accepting connections (the proxy server throws “Connection refused”).
Grafana logs go silent and only after a grafana-server process restart everything is back to normal.

Any thoughts?