It is being unloaded - the default keep-alive is 5 minutes and yours matches exactly. Do not buy a drive, change a setting.
Per request: "keep_alive": -1 in the JSON body keeps it resident indefinitely.
Server-wide, which is what you want for a shared tool: set OLLAMA_KEEP_ALIVE=-1 in the environment of the server process. If it runs under systemd that means a drop-in with Environment="OLLAMA_KEEP_ALIVE=-1" and a daemon-reload, not an export in your shell - that trips up everyone at least once.
Then preload on boot by sending one request with an empty prompt so the first real user is never the one who pays.