When does an API key stop working?

As soon as an Owner chooses Revoke next to it in Company settings (click your picture at the top right, then Company settings). A key also stops working when the person who made it is no longer an Owner, and pauses while your company isn't on Pro.

Changes made with a key are recorded in Activity as made by the person who made the key. The list of keys shows when each was last used, so you can spot the ones nobody needs.