"That's surprising because presumably they lose all results if they have to reboot the server."
Strictly speaking they only lose all results, FOR SURE, if they have to reboot ALL the servers at the same time. If they implemented a system where the cached results are shared and replicated among all their servers, it can in theory be kept cached indefinitely.
From the FAQ:
> Each time the Leta application is restarted (due to an upgrade, or new version) server side, a new secret hash is generated, meaning that all previous search queries are no longer visible to Leta.
If I read this correctly, the cached data is per-instance, there would be no way to share cached data among instances if each one has its own secret hash and they are cycled on each start.