Stations take themselves off air after ten minutes of producing no audio with nothing attached that could start producing some. That is the whole rule, and it explains almost every case of a station stopping on its own.

What Does Not Cause It

Having no listeners. Listener count plays no part in this decision at all. A rotation playing to an empty room is exactly the thing you are paying for, and stopping it would be an outage rather than a saving. Your station will happily play to nobody indefinitely.

A muted microphone. Once you are connected, you are connected. Dead air while you find a record does not stop your station, and neither does a five-minute silence you left on purpose.

What Does Cause It

Switching on and then not connecting. The classic: you put the station on air, went to set up your encoder, and took more than ten minutes. Nothing was attached and nothing was playing, so it reads exactly like an abandoned station.
Ending a live broadcast with no AutoDJ. On the free plan there is nothing to fall back to, so the station goes quiet and then stops. This is normal and not a fault — it is how the free plan works.
An empty or broken rotation. AutoDJ with nothing in it produces silence, and silence with nothing to play is an idle station.

If It Stopped With a Full Rotation

That is different, and we want to know about it. A station that had music to play and was emitting nothing is a fault, not an idle station, and the system can tell the two apart. Email hello@gocast.fm with your station name and roughly when it happened.

Avoiding It

Connect your encoder first and switch the station on second, or at least do the two close together. If you want a station that is simply always up, give it a default playlist with something in it — a station with audio to play is never stopped by this.