I've experienced this as well. I gave up on optimizing it.

I get around it by using a load balancer (Cloudflare currently) that does periodic health checks. Keeps it alive and the charges are minimal (still well within the free tier).

Speaking of Cloudflare it's on my "nice to-do" list to move this to Workers as a primary anyway.

I also use a completely separate uptime monitor and alerting platform (Uptime Robot) so one way or another I'd be keeping at least one instance warm no matter what.