Cockroaches have an incredibly slow metabolism compared to most insects, which means they burn through stored energy far more gradually than you'd expect. A cockroach's body is built to conserve resources, slowing down its bodily functions considerably when food becomes scarce rather than rushing to find more straight away.
This adaptation traces back millions of years, long before humans existed to leave crumbs on kitchen benches. Cockroaches evolved in environments where food wasn't always guaranteed, and that evolutionary history is exactly why a month without eating barely registers as a crisis for them.