You lose the station if your reputation falls to 0%.
Check the station report (it is available by clicking on the percentage next to the smiley face in the bar across the top of the screen but the daily report will also pop up on the screen at the end of each day). This will help you see where you are gaining and losing rep in your station. (see screenshot)
Sometimes a situation may be occurring in your station that is causing you to lose a lot of rep very quickly. The game does not notify you of rep loss (besides the percentage at the top of the screen) – you will only get a notification if your rep falls below 20%. If this is happening, pause the game and find out where the problem is that is causing the rep loss. Sometimes it is throughout the entire station (i.e. high litter) or sometimes it is happening in one specific area. If it is happening in one area, consider installing an alarm and using it to evacuate people from the area. This will hopefully allow you to get a handle on the situation and stop reputation from continuing to drop.