All limit orders are Good 'Til Cancelled (GTC) meaning that they stay on the order book until they have been completely filled or until you manually cancel them.
If you are trading programmatically via the Gemini API, you can enable a feature called "Require Heartbeat," which will automatically cancel all of your open orders if you lose connectivity to Gemini. This feature can be found on our API Settings page.
*Currently limit orders on the mobile app are only available to a subset of customers via a pilot program.