It is not always that clear. The Suunto Stinger manual claims the computer will "look you out" for 24hours. That, however, does not mean that the device stops working altogether (as I interpreted initially), it means that it will no longer give you information on NDL time remaining and so on until you have stopped diving with it for 24hours.
I found that the Suuntos are extremely conservative. In one occasion I went slightly over the NDL, but the time the stinger wanted me to stay in the shallows was impractical in the circumstances, and was also a very very conservative value. I decided to cut short the shallows time and the computer was very unhappy. For the rest of the trip the suunto defaulted to a "gauge" mode which only indicated depth and time ... which suited me just fine
I am NOT advocating that you ignore your computer's advice. However, it is worth being a "thinking" user of a computer. A violation of the NDLs is not a binary event and you should know something about the model inside the computer and what assumptions it is making. For example, the suunto is programmed for the safety stop to last 3 minutes and to happen between 4 and 6 m (I think, if has been a while). If you follow a strategy of doing 1 minute stops every 3 m from half depth (as taught by some agencies), you end being forced by the computer model to perform an extra safety stop ... it won't hurt, but it is also somewhat overkill.